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 A294842 #10 Feb 16 2025 08:33:51
%S A294842 1,1,6,24,73,238,722,2175,6343,18177,50982,140671,382227,1023623,
%T A294842 2706184,7067324,18250671,46635309,117997008,295794098,735030985,
%U A294842 1811435607,4429226677,10749552338,25903858181,62000039513,147435739522,348431110651,818549931526,1912010876019,4441687009798
%N A294842 Expansion of Product_{k>=1} (1 + x^k)^(k^2*(k+1)/2).
%C A294842 Weigh transform of the pentagonal pyramidal numbers (A002411).
%H A294842 Vaclav Kotesovec, <a href="/A294842/b294842.txt">Table of n, a(n) for n = 0..2000</a>
%H A294842 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 A294842 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 A294842 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A294842 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentagonalPyramidalNumber.html">Pentagonal Pyramidal Number</a>
%F A294842 G.f.: Product_{k>=1} (1 + x^k)^A002411(k).
%F A294842 a(n) ~ exp(-2401 * Pi^16 / (2^12 * 3^11 * 5^8 * Zeta(5)^3) + (343 * Pi^12 / (2^(38/5) * 3^(37/5) * 5^(36/5) * Zeta(5)^(11/5))) * n^(1/5) - (49*Pi^8 / (2^(31/5) * 3^(24/5) * 5^(22/5) * Zeta(5)^(7/5))) * n^(2/5) + (7*Pi^4 / (2^(14/5) * 3^(16/5) * 5^(8/5) * Zeta(5)^(3/5))) * n^(3/5) + (5 * 3^(2/5) * (5*Zeta(5))^(1/5) / 2^(12/5)) * n^(4/5)) * 3^(1/5) * Zeta(5)^(1/10) / (2^(167/240) * 5^(2/5) * sqrt(Pi) * n^(3/5)). - _Vaclav Kotesovec_, Nov 10 2017
%t A294842 nmax = 30; CoefficientList[Series[Product[(1 + x^k)^(k^2 (k + 1)/2), {k, 1, nmax}], {x, 0, nmax}], x]
%t A294842 a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d + 1) d^3 (d + 1)/2, {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 30}]
%Y A294842 Cf. A002411, A258343, A281156, A294102, A294839, A294843, A294844, A294845.
%K A294842 nonn
%O A294842 0,3
%A A294842 _Ilya Gutkovskiy_, Nov 09 2017