The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A278768 Expansion of Product_{k>=1} 1/(1 - x^k)^(k*(3*k-1)/2). 8
 1, 1, 6, 18, 55, 150, 424, 1113, 2923, 7401, 18510, 45271, 109297, 259447, 608428, 1407958, 3222132, 7292198, 16340830, 36265672, 79775931, 173999194, 376497975, 808471181, 1723592762, 3649271887, 7675809680, 16043777217, 33332888108, 68853608216, 141438908854, 288994878713, 587458691042 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Euler transform of the pentagonal numbers (A000326). LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..5000 M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version] M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures] N. J. A. Sloane, Transforms Eric Weisstein's World of Mathematics, Pentagonal Number Index to sequences related to polygonal numbers FORMULA G.f.: Product_{k>=1} 1/(1 - x^k)^(k*(3*k-1)/2). a(n) ~ exp(-Zeta'(-1)/2 - 3*Zeta(3)/(8*Pi^2) - 25*Zeta(3)^3/(6*Pi^8) - 5^(5/4)*Zeta(3)^2/(2^(7/4)*Pi^5) * n^(1/4) - sqrt(5/2)*Zeta(3)/Pi^2 * sqrt(n) + 2^(7/4)*Pi/(3*5^(1/4)) * n^(3/4)) / (2^(155/96) * 5^(11/96) * Pi^(1/24) * n^(59/96)). - Vaclav Kotesovec, Dec 02 2016 MAPLE with(numtheory): a:= proc(n) option remember; `if`(n=0, 1, add(add( d^2*(3*d-1)/2, d=divisors(j))*a(n-j), j=1..n)/n) end: seq(a(n), n=0..35); # Alois P. Heinz, Dec 02 2016 MATHEMATICA nmax=32; CoefficientList[Series[Product[1/(1 - x^k)^(k (3 k - 1)/2), {k, 1, nmax}], {x, 0, nmax}], x] CROSSREFS Cf. A000294, A000326, A000335, A023871. Sequence in context: A292295 A183913 A056349 * A035070 A075386 A056343 Adjacent sequences: A278765 A278766 A278767 * A278769 A278770 A278771 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Nov 28 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 14 23:20 EDT 2024. Contains 373401 sequences. (Running on oeis4.)