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 A278949 #13 Feb 16 2025 08:33:37
%S A278949 1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,9,9,11,11,11,
%T A278949 12,13,13,15,15,15,16,17,17,19,20,20,23,24,24,26,27,27,30,31,31,33,34,
%U A278949 35,38,40,40,44,45,46,49,51,51,56,57,58,61,63,64,69,72,73,78,80,81,86,89,90,96,98,99,105,108,110,116,120,121,130
%N A278949 Expansion of Product_{k>=1} 1/(1 - x^(k*(2*k-1))).
%C A278949 Number of partitions of n into nonzero hexagonal numbers (A000384).
%H A278949 Alois P. Heinz, <a href="/A278949/b278949.txt">Table of n, a(n) for n = 0..20000</a>
%H A278949 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 A278949 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 A278949 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HexagonalNumber.html">Hexagonal Number</a>
%H A278949 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%H A278949 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A278949 G.f.: Product_{k>=1} 1/(1 - x^(k*(2*k-1))).
%e A278949 a(7) = 2 because we have [6, 1] and [1, 1, 1, 1, 1, 1, 1].
%p A278949 h:= proc(n) option remember; `if`(n<1, 0, (t->
%p A278949 `if`(t*(2*t-1)>n, t-1, t))(1+h(n-1)))
%p A278949 end:
%p A278949 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A278949 b(n, i-1)+(t-> b(n-t, min(i, h(n-t))))(i*(2*i-1))))
%p A278949 end:
%p A278949 a:= n-> b(n, h(n)):
%p A278949 seq(a(n), n=0..100); # _Alois P. Heinz_, Dec 28 2018
%t A278949 nmax=90; CoefficientList[Series[Product[1/(1 - x^(k (2 k - 1))), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A278949 Cf. A000384, A001156, A007294, A037444, A218379.
%K A278949 nonn,easy
%O A278949 0,7
%A A278949 _Ilya Gutkovskiy_, Dec 02 2016