This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A295179 #9 Feb 16 2025 08:33:52
%S A295179 1,1,5,15,44,115,312,790,2004,4908,11885,28170,65987,152079,346560,
%T A295179 779808,1736460,3825995,8351733,18064545,38747740,82443251,174096564,
%U A295179 364991008,759989218,1572126699,3231929735,6604498620,13419469596,27117216441,54508611399,109013531864,216956853105
%N A295179 Expansion of Product_{k>=1} 1/(1 - x^k)^(3*k*(k-1)/2+1).
%C A295179 Euler transform of the centered triangular numbers (A005448).
%H A295179 Vaclav Kotesovec, <a href="/A295179/b295179.txt">Table of n, a(n) for n = 0..4000</a>
%H A295179 M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
%H A295179 M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
%H A295179 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A295179 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CenteredTriangularNumber.html">Centered Triangular Number</a>
%H A295179 <a href="/index/Ce#CENTRALCUBE">Index entries for sequences related to centered polygonal numbers</a>
%F A295179 G.f.: Product_{k>=1} 1/(1 - x^k)^A005448(k).
%F A295179 a(n) ~ exp(-3*Zeta'(-1)/2 + 7*Zeta(3) / (8*Pi^2) - 225*Zeta(3)^3 / (2*Pi^8) + (Pi / (3*2^(3/4)) - 45*Zeta(3)^2 / (2^(7/4) * Pi^5)) * (5*n)^(1/4) - (3*sqrt(5/2) * Zeta(3) / Pi^2) * sqrt(n) + (2^(7/4)*Pi / (3*5^(1/4))) * n^(3/4)) / (2^(71/32) * 5^(7/32) * Pi^(1/8) * n^(23/32)). - _Vaclav Kotesovec_, Nov 16 2017
%t A295179 nmax = 32; CoefficientList[Series[Product[1/(1 - x^k)^(3 k (k - 1)/2 + 1), {k, 1, nmax}], {x, 0, nmax}], x]
%t A295179 a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d (3 d (d - 1)/2 + 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 32}]
%Y A295179 Cf. A000294, A000335, A005448, A295180.
%K A295179 nonn
%O A295179 0,3
%A A295179 _Ilya Gutkovskiy_, Nov 16 2017