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 A280950 #12 Feb 16 2025 08:33:39
%S A280950 1,1,1,1,2,2,2,2,3,3,4,4,5,5,6,6,7,7,8,9,11,11,12,13,15,15,16,17,19,
%T A280950 20,22,24,26,27,29,31,33,34,37,40,43,45,48,51,54,56,60,63,67,70,76,80,
%U A280950 84,87,93,97,102,106,113,118,125,130,138,143,151,157,166,172,181,189,200,207,217,225,237,245,257,267,280
%N A280950 Expansion of Product_{k>=0} 1/(1 - x^(3*k*(k+1)/2+1)).
%C A280950 Number of partitions of n into centered triangular numbers (A005448).
%H A280950 Robert Israel, <a href="/A280950/b280950.txt">Table of n, a(n) for n = 0..10000</a>
%H A280950 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 A280950 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 A280950 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CenteredTriangularNumber.html">Centered Triangular Number</a>
%H A280950 <a href="/index/Ce#CENTRALCUBE">Index entries for sequences related to centered polygonal numbers</a>
%H A280950 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A280950 G.f.: Product_{k>=0} 1/(1 - x^(3*k*(k+1)/2+1)).
%e A280950 a(8) = 3 because we have [4, 4], [4, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1].
%p A280950 N:= 100:
%p A280950 kmax:= floor((sqrt(24*N-15)-3)/6):
%p A280950 S:= series(mul(1/(1-x^(3*k*(k+1)/2+1)),k=0..kmax),x,N+1):
%p A280950 seq(coeff(S,x,j),j=0..N); # _Robert Israel_, Jan 25 2017
%t A280950 nmax = 78; CoefficientList[Series[Product[1/(1 - x^(3 k (k + 1)/2 + 1)), {k, 0, nmax}], {x, 0, nmax}], x]
%Y A280950 Cf. A005448, A007294, A068980, A280951, A280952, A280953.
%K A280950 nonn
%O A280950 0,5
%A A280950 _Ilya Gutkovskiy_, Jan 11 2017