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 A261775 #36 Aug 07 2022 19:55:06
%S A261775 1,1,2,3,5,7,11,15,21,29,40,53,72,94,124,161,208,266,341,431,545,684,
%T A261775 856,1064,1322,1631,2009,2464,3014,3672,4467,5411,6543,7888,9489,
%U A261775 11383,13632,16280,19409,23088,27415,32483,38430,45371,53485,62939,73950,86742
%N A261775 Expansion of Product_{k>=1} (1 - x^(8*k))/(1 - x^k).
%C A261775 Number of partitions in which no part occurs more than 7 times. - _Ilya Gutkovskiy_, May 31 2017
%H A261775 Seiichi Manyama, <a href="/A261775/b261775.txt">Table of n, a(n) for n = 0..10000</a>
%H A261775 P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/books.html">Analytic Combinatorics</a>, 2009; see page 30
%H A261775 Vaclav Kotesovec, <a href="http://arxiv.org/abs/1509.08708">A method of finding the asymptotics of q-series based on the convolution of generating functions</a>, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 15.
%F A261775 a(n) ~ Pi*sqrt(7) * BesselI(1, sqrt(7*(24*n + 7)/8) * Pi/6) / (4*sqrt(24*n + 7)) ~ exp(Pi*sqrt(7*n/3)/2) * 7^(1/4) / (2^(7/2) * 3^(1/4) * n^(3/4)) * (1 + (7^(3/2)*Pi/(96*sqrt(3)) - 3*sqrt(3)/(4*Pi*sqrt(7))) / sqrt(n) + (343*Pi^2/55296 - 45/(224*Pi^2) - 35/128) / n). - _Vaclav Kotesovec_, Aug 31 2015, extended Jan 14 2017
%F A261775 a(n) = (1/n)*Sum_{k=1..n} A284341(k)*a(n-k), a(0) = 1. - _Seiichi Manyama_, Mar 25 2017
%F A261775 G.f.: A(x)*A(x^2)*A(x^4) where A(x) is the o.g.f. for A000009. (see Flajolet, Sedgewick link) - _Geoffrey Critzer_, Aug 07 2022
%p A261775 a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*add(d*
%p A261775 signum(irem(d, 8)), d=numtheory[divisors](j)), j=1..n)/n)
%p A261775 end:
%p A261775 seq(a(n), n=0..50); # _Alois P. Heinz_, Aug 07 2022
%t A261775 nmax = 50; CoefficientList[Series[Product[(1 - x^(8*k))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%t A261775 Table[Count[IntegerPartitions@n, x_ /; ! MemberQ [Mod[x, 8], 0, 2] ], {n, 0, 47}] (* _Robert Price_, Jul 28 2020 *)
%o A261775 (PARI) Vec(prod(k=1, 51, (1 - x^(8*k))/(1 - x^k)) + O(x^51)) \\ _Indranil Ghosh_, Mar 25 2017
%Y A261775 Number of r-regular partitions for r = 2 through 12: A000009, A000726, A001935, A035959, A219601, A035985, A261775, A104502, A261776, A328545, A328546.
%Y A261775 Cf. A261771, A261735, A320610.
%K A261775 nonn
%O A261775 0,3
%A A261775 _Vaclav Kotesovec_, Aug 31 2015