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A000391
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Euler transform of A000332.
(Formerly M4144 N1721)
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17
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1, 6, 21, 71, 216, 672, 1982, 5817, 16582, 46633, 128704, 350665, 941715, 2499640, 6557378, 17024095, 43756166, 111433472, 281303882, 704320180, 1749727370, 4314842893, 10565857064, 25700414815, 62115621317, 149214574760, 356354881511, 846292135184
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..500
A. O. L. Atkin, P. Bratley, I. G. McDonald and J. K. S. McKay, Some computations for m-dimensional partitions, Proc. Camb. Phil. Soc., 63 (1967), 1097-1100.
A. O. L. Atkin, P. Bratley, I. G. McDonald and J. K. S. McKay, Some computations for m-dimensional partitions, Proc. Camb. Phil. Soc., 63 (1967), 1097-1100. [Annotated scanned copy]
Srivatsan Balakrishnan, Suresh Govindarajan and Naveen S. Prabhakar, On the asymptotics of higher-dimensional partitions, arXiv:1105.6231, p.21.
N. J. A. Sloane, Transforms
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FORMULA
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a(n) ~ Pi^(3/160) / (2 * 3^(243/320) * 7^(83/960) * n^(563/960)) * exp(Zeta'(-1)/4 - 143 * Zeta(3) / (240 * Pi^2) + 53461 * Zeta(5) / (3200 * Pi^4) + 107163 * Zeta(3) * Zeta(5)^2 / (2*Pi^12) - 24754653 * Zeta(5)^3 / (10*Pi^14) + 413420708484 * Zeta(5)^5 / (5*Pi^24) + Zeta'(-3)/4 + (-847 * 7^(1/6) * Pi / (19200 * sqrt(3)) - 189 * sqrt(3) * 7^(1/6) * Zeta(3) * Zeta(5) / (2*Pi^7) + 305613 * sqrt(3) * 7^(1/6) * Zeta(5)^2 / (80*Pi^9) - 614365479 * sqrt(3) * 7^(1/6) * Zeta(5)^4 / (4*Pi^19)) * n^(1/6) + (3 * 7^(1/3) * Zeta(3) / (4*Pi^2) - 693 * 7^(1/3) * Zeta(5) / (40*Pi^4) + 857304 * 7^(1/3) * Zeta(5)^3 / Pi^14) * n^(1/3) + (11 * sqrt(7/3) * Pi / 120 - 1701 * sqrt(21) * Zeta(5)^2 / Pi^9) * sqrt(n) + 27 * 7^(2/3) * Zeta(5) / (2*Pi^4) * n^(2/3) + 2*sqrt(3)*Pi / (5*7^(1/6)) * n^(5/6)). - Vaclav Kotesovec, Mar 12 2015
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MAPLE
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with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d, j; if n=0 then 1 else add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: a:= etr(n-> binomial(n+3, 4)): seq(a(n), n=1..30); # Alois P. Heinz, Sep 08 2008
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MATHEMATICA
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nn = 50; b = Table[Binomial[n, 4], {n, 4, nn + 4}]; Rest[CoefficientList[Series[Product[1/(1 - x^m)^b[[m]], {m, nn}], {x, 0, nn}], x]] (* T. D. Noe, Jun 21 2012 *)
nmax=50; Rest[CoefficientList[Series[Product[1/(1-x^k)^(k*(k+1)*(k+2)*(k+3)/24), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Mar 11 2015 *)
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PROG
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(PARI) a(n)=if(n<0, 0, polcoeff(exp(sum(k=1, n, x^k/(1-x^k)^5/k, x*O(x^n))), n)) /* Joerg Arndt, Apr 16 2010 */
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CROSSREFS
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Cf. A000041, A000219, A000294, A000335, A000417, A000428, A255965.
Sequence in context: A101904 A022814 A000390 * A360090 A107660 A200665
Adjacent sequences: A000388 A000389 A000390 * A000392 A000393 A000394
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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