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 A279012 #12 Feb 16 2025 08:33:37
%S A279012 1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,4,4,4,5,5,5,5,6,6,6,7,7,7,7,8,8,
%T A279012 9,10,11,11,11,12,12,13,14,15,15,15,16,16,17,18,19,19,20,21,22,24,25,
%U A279012 26,26,27,28,29,31,32,33,33,34,35,37,39,41,42,43,45,46,48,50,52,53,54,56,58,60,62,64,65,67,69,72,75,78
%N A279012 Expansion of Product_{k>=1} 1/(1 - x^(k*(5*k-3)/2)).
%C A279012 Number of partitions of n into nonzero heptagonal numbers (A000566).
%H A279012 Alois P. Heinz, <a href="/A279012/b279012.txt">Table of n, a(n) for n = 0..20000</a>
%H A279012 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 A279012 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 A279012 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeptagonalNumber.html">Heptagonal Number</a>
%H A279012 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%H A279012 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A279012 G.f.: Product_{k>=1} 1/(1 - x^(k*(5*k-3)/2)).
%e A279012 a(8) = 2 because we have [7, 1] and [1, 1, 1, 1, 1, 1, 1, 1].
%p A279012 h:= proc(n) option remember; `if`(n<1, 0, (t->
%p A279012 `if`(t*(5*t-3)/2>n, t-1, t))(1+h(n-1)))
%p A279012 end:
%p A279012 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A279012 b(n, i-1)+(t-> b(n-t, min(i, h(n-t))))(i*(5*i-3)/2)))
%p A279012 end:
%p A279012 a:= n-> b(n, h(n)):
%p A279012 seq(a(n), n=0..100); # _Alois P. Heinz_, Dec 28 2018
%t A279012 nmax=90; CoefficientList[Series[Product[1/(1 - x^(k (5 k - 3)/2)), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A279012 Cf. A000566, A001156, A007294, A037444, A218379, A278949.
%K A279012 nonn,easy
%O A279012 0,8
%A A279012 _Ilya Gutkovskiy_, Dec 03 2016