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A000428
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Euler transform of A000579.
(Formerly M4519 N1913)
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12
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1, 8, 36, 148, 554, 2094, 7624, 27428, 96231, 332159, 1126792, 3769418, 12437966, 40544836, 130643734, 416494314, 1314512589, 4110009734, 12737116845, 39144344587, 119350793207, 361173596536, 1085171968872
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OFFSET
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1,2
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COMMENTS
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In general, if g.f. = Product_{k>=1} 1/(1-x^k)^binomial(k+m-2,m-1) and m >= 1, then log(a(n)) ~ (m+1) * Zeta(m+1)^(1/(m+1)) * (n/m)^(m/(m+1)). - Vaclav Kotesovec, Mar 12 2015
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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..1000
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]
Vaclav Kotesovec, Asymptotic formula
N. J. A. Sloane, Transforms
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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+5, 6)): seq(a(n), n=1..30); # Alois P. Heinz, Sep 08 2008
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MATHEMATICA
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nn = 30; b = Table[Binomial[n, 6], {n, 6, nn + 6}]; Rest[CoefficientList[Series[Product[1/(1 - x^m)^b[[m]], {m, nn}], {x, 0, nn}], x]] (* T. D. Noe, Jun 20 2012 *)
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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)^7/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, A000391, A000417, A255965.
Sequence in context: A119767 A024208 A000427 * A083597 A178744 A200707
Adjacent sequences: A000425 A000426 A000427 * A000429 A000430 A000431
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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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