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 A280952 #12 Feb 16 2025 08:33:39
%S A280952 1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,4,4,5,5,5,5,6,6,7,7,7,7,8,8,9,10,11,
%T A280952 11,12,12,13,14,15,15,16,16,17,18,19,19,20,21,23,24,25,26,27,28,30,31,
%U A280952 32,33,34,35,37,38,40,42,44,45,47,49,51,53,55,56,58,60,62,64,67,68,71,74,77,79,83,85,88,91,94,96,100
%N A280952 Expansion of Product_{k>=0} 1/(1 - x^(5*k*(k+1)/2+1)).
%C A280952 Number of partitions of n into centered pentagonal numbers (A005891).
%H A280952 Alois P. Heinz, <a href="/A280952/b280952.txt">Table of n, a(n) for n = 0..20000</a>
%H A280952 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 A280952 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 A280952 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CenteredPentagonalNumber.html">Centered Pentagonal Number</a>
%H A280952 <a href="/index/Ce#CENTRALCUBE">Index entries for sequences related to centered polygonal numbers</a>
%H A280952 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A280952 G.f.: Product_{k>=0} 1/(1 - x^(5*k*(k+1)/2+1)).
%e A280952 a(12) = 3 because we have [6, 6], [6, 1, 1, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
%p A280952 h:= proc(n) option remember; `if`(n<0, 0, (t->
%p A280952 `if`(((t+1)*5*t+2)/2>n, t-1, t))(1+h(n-1)))
%p A280952 end:
%p A280952 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<0, 0,
%p A280952 b(n, i-1)+(t-> b(n-t, min(i, h(n-t))))(((i+1)*5*i+2)/2)))
%p A280952 end:
%p A280952 a:= n-> b(n, h(n)):
%p A280952 seq(a(n), n=0..100); # _Alois P. Heinz_, Dec 28 2018
%t A280952 nmax = 88; CoefficientList[Series[Product[1/(1 - x^(5 k (k + 1)/2 + 1)), {k, 0, nmax}], {x, 0, nmax}], x]
%Y A280952 Cf. A005891, A218379, A279221, A280950, A280951, A280953.
%K A280952 nonn
%O A280952 0,7
%A A280952 _Ilya Gutkovskiy_, Jan 11 2017