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 A294654 #10 Feb 16 2025 08:33:51
%S A294654 1,1,5,12,35,81,208,475,1123,2505,5617,12192,26368,55797,117255,
%T A294654 242660,498126,1010515,2033662,4053214,8017622,15729219,30643069,
%U A294654 59268267,113898873,217480476,412813600,779042099,1462188257,2729852845,5070966794,9373909586,17247473718
%N A294654 Expansion of Product_{k>=1} 1/((1 - x^(2*k-1))^(k*(5*k-3)/2)*(1 - x^(2*k))^(k*(5*k+3)/2)).
%C A294654 Euler transform of the generalized heptagonal numbers (A085787).
%H A294654 Vaclav Kotesovec, <a href="/A294654/b294654.txt">Table of n, a(n) for n = 0..5000</a>
%H A294654 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A294654 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeptagonalNumber.html">Heptagonal Number</a>
%F A294654 G.f.: Product_{k>=1} 1/(1 - x^k)^A085787(k).
%F A294654 a(n) ~ exp(Pi * (2/3)^(5/4) * n^(3/4) + 5*Zeta(3) * sqrt(3*n) / (2^(3/2) * Pi^2) - (75*3^(1/4) * Zeta(3)^2 / (2^(13/4) * Pi^5) + Pi / (2^(17/4) * 3^(3/4))) * n^(1/4) + 375 * Zeta(3)^3 / (8*Pi^8) - 5*Zeta(3) / (64*Pi^2) + 1/12) * Pi^(1/12) / (A * 2^(11/6) * 3^(7/48) * n^(31/48)), where A is the Glaisher-Kinkelin constant A074962. - _Vaclav Kotesovec_, Nov 07 2017
%t A294654 nmax = 32; CoefficientList[Series[Product[1/((1 - x^(2 k - 1))^(k (5 k - 3)/2) (1 - x^(2 k))^(k (5 k + 3)/2)), {k, 1, nmax}], {x, 0, nmax}], x]
%t A294654 a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d (5 d (d + 1)/8 + (-1)^d (2 d + 1)/16 - 1/16), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 32}]
%Y A294654 Cf. A000294, A085787, A278769, A294591, A294621, A294655.
%K A294654 nonn
%O A294654 0,3
%A A294654 _Ilya Gutkovskiy_, Nov 06 2017