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 A298311 #17 Jul 21 2025 21:41:25
%S A298311 1,3,7,16,32,61,112,197,336,560,912,1456,2287,3536,5392,8123,12096,
%T A298311 17824,26016,37632,53984,76848,108601,152432,212592,294704,406201,
%U A298311 556864,759488,1030784,1392496,1872784,2508048,3345184,4444384,5882747,7758736,10197712,13358944,17444256,22708719
%N A298311 Expansion of Product_{k>=1} 1/((1 - x^(2*k))*(1 - x^(2*k-1))^3).
%C A298311 Number of partitions of n where there are 3 kinds of odd parts.
%C A298311 Convolution of the sequences A000009 and A015128.
%H A298311 Michael D. Hirschhorn and James A. Sellers, <a href="https://arxiv.org/abs/2507.09752">A Family of Congruences Modulo 7 for Partitions with Monochromatic Even Parts and Multi-Colored Odd Parts</a>, arXiv:2507.09752 [math.CO], 2025. See p. 2.
%H A298311 <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F A298311 G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 - x^(2*k-1))^3).
%F A298311 G.f.: Product_{k>=1} (1 + x^k)^2/(1 - x^k).
%F A298311 a(n) ~ exp(2*Pi*sqrt(n/3)) / (2^(5/2)*sqrt(3)*n). - _Vaclav Kotesovec_, Apr 08 2018
%F A298311 G.f.: 1/Product_{n > = 1} ( 1 - x^(n/gcd(n,k)) ) for k = 4. Cf. A000041 (k = 1), A015128 (k = 2), A278690 (k = 3) and A160461 (k = 5). - _Peter Bala_, Nov 17 2020
%t A298311 nmax = 40; CoefficientList[Series[Product[1/((1 - x^(2 k)) (1 - x^(2 k - 1))^3), {k, 1, nmax}], {x, 0, nmax}], x]
%t A298311 nmax = 40; CoefficientList[Series[Product[(1 + x^k)^2/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A298311 Cf. A000009, A000041, A000716, A015128, A029862, A029863, A160461, A182818, A278690.
%K A298311 nonn,easy
%O A298311 0,2
%A A298311 _Ilya Gutkovskiy_, Jan 17 2018