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 A000417 Euler transform of A000389. (Formerly M4392 N1849) 13
 1, 7, 28, 105, 357, 1232, 4067, 13301, 42357, 132845, 409262, 1243767, 3727360, 11036649, 32300795, 93538278, 268164868, 761656685, 2144259516, 5986658951, 16583102077, 45593269265, 124464561544, 337479729179, 909156910290, 2434121462871, 6478440788169 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES 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). LINKS 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] N. J. A. Sloane, Transforms FORMULA a(n) ~ (3*Zeta(7))^(31103/423360) / (2^(180577/423360) * sqrt(7*Pi) * n^(242783/423360)) * exp(Zeta'(-1)/5 - 5*Zeta(3)/(48*Pi^2) + Zeta(5)/(16*Pi^4) - Pi^36/(1162964338810860915 * Zeta(7)^5) + Pi^24 * Zeta(5) / (413420708484 * Zeta(7)^4) - Pi^22 / (137806902828 * Zeta(7)^3) - Pi^12 * Zeta(5)^2 / (551124 * Zeta(7)^3) + Pi^12 * Zeta(3) / (11252115 * Zeta(7)^2) + Pi^10 * Zeta(5) / (122472 * Zeta(7)^2) + 49*Zeta(5)^3 / (216 * Zeta(7)^2) - Pi^8 / (108864 * Zeta(7)) - Zeta(3) * Zeta(5) / (15*Zeta(7)) + Zeta'(-5)/120 + 7*Zeta'(-3)/24 + (22 * 2^(6/7) * Pi^30 / (46901442470561469 * 3^(1/7) * Zeta(7)^(29/7)) - 10 * 2^(6/7) * Pi^18 * Zeta(5) / (8931928887 * 3^(1/7) * Zeta(7)^(22/7)) + Pi^16 / (141776649 * 6^(1/7) * Zeta(7)^(15/7)) + 2^(6/7) * Pi^6 * Zeta(5)^2 / (1701 * 3^(1/7) * Zeta(7)^(15/7)) - 2^(6/7) * Pi^6 * Zeta(3) / (19845 * 3^(1/7) * Zeta(7)^(8/7)) - Pi^4 * Zeta(5) / (216 * 6^(1/7) * Zeta(7)^(8/7))) * n^(1/7) + (-2 * 2^(5/7) * Pi^24 / (3938980639167 * 3^(2/7) * Zeta(7)^(23/7)) + Pi^12 * Zeta(5) / (500094 * 6^(2/7) * Zeta(7)^(16/7)) - Pi^10 / (142884 * 6^(2/7) * Zeta(7)^(9/7)) - 7*Zeta(5)^2 / (12 * 6^(2/7) * Zeta(7)^(9/7)) + Zeta(3)/(5 * (6*Zeta(7))^(2/7))) * n^(2/7) + (5 * 2^(4/7) * Pi^18 / (8931928887 * 3^(3/7) * Zeta(7)^(17/7)) - Pi^6 * Zeta(5) / (567 * 6^(3/7) * Zeta(7)^(10/7)) + Pi^4 / (108 * (6*Zeta(7))^(3/7))) * n^(3/7) + (-Pi^12 / (750141 * 6^(4/7) * Zeta(7)^(11/7)) + 7*Zeta(5) / (4 * (6 * Zeta(7))^(4/7))) * n^(4/7) + 2^(2/7) * Pi^6 / (945 * (3*Zeta(7))^(5/7)) * n^(5/7) + 7*Zeta(7)^(1/7) / 6^(6/7) * n^(6/7)). - Vaclav Kotesovec, Mar 12 2015 MAPLE 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+4, 5)): seq(a(n), n=1..30); # Alois P. Heinz, Sep 08 2008 MATHEMATICA nn = 100; b = Table[Binomial[n, 5], {n, 5, nn + 5}]; Rest[CoefficientList[Series[Product[1/(1 - x^m)^b[[m]], {m, nn}], {x, 0, nn}], x]] (* T. D. Noe, Jun 20 2012 *) PROG (PARI) a(n)=if(n<0, 0, polcoeff(exp(sum(k=1, n, x^k/(1-x^k)^6/k, x*O(x^n))), n)) /* Joerg Arndt, Apr 16 2010 */ CROSSREFS Cf. A000041, A000219, A000294, A000335, A000391, A000428, A255965. Sequence in context: A331197 A024207 A000416 * A200762 A243150 A344206 Adjacent sequences: A000414 A000415 A000416 * A000418 A000419 A000420 KEYWORD nonn AUTHOR EXTENSIONS More terms from Sean A. Irvine, Nov 14 2010 STATUS approved

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Last modified March 31 15:55 EDT 2023. Contains 361668 sequences. (Running on oeis4.)