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 A381679 #25 Apr 01 2025 12:01:40
%S A381679 1,1,7,31,100,364,1152,3864,12102,37358,113618,337562,990798,2857926,
%T A381679 8144334,22902470,63660695,175026047,476242001,1283435153,3427047146,
%U A381679 9072455146,23820491998,62057045134,160471504373,412022656517,1050740365571,2662223436203
%N A381679 Euler transform of A000056.
%H A381679 Vaclav Kotesovec, <a href="/A381679/b381679.txt">Table of n, a(n) for n = 0..5000</a>
%F A381679 G.f.: 1/Product_{k>=1} (1 - x^k)^A000056(k).
%F A381679 G.f.: exp( Sum_{k>=1} sigma_4(k^2)/sigma_2(k^2) * x^k/k ).
%F A381679 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} sigma_4(k^2)/sigma_2(k^2) * a(n-k).
%F A381679 a(n) ~ exp(5*(3*zeta(5)/zeta(3))^(1/5) * n^(4/5) / 2^(7/5) - 1/10 - 12*zeta'(-3)) * A^(6/5) * (3*zeta(5)/zeta(3))^(3/25) / (2^(7/50) * sqrt(5*Pi) * n^(31/50)), where A is the Glaisher-Kinkelin constant A074962. - _Vaclav Kotesovec_, Mar 04 2025
%t A381679 a[0] = 1; a[n_] := a[n] = Sum[DivisorSigma[4, k^2]/DivisorSigma[2, k^2]*a[n-k], {k, 1, n}]/n; Table[a[n], {n, 0, 30}] (* _Vaclav Kotesovec_, Mar 04 2025 *)
%o A381679 (PARI) my(N=30, x='x+O('x^N)); Vec(exp(sum(k=1, N, sigma(k^2, 4)/sigma(k^2, 2)*x^k/k)))
%Y A381679 Cf. A061255, A381680.
%Y A381679 Cf. A000056, A084218, A156733.
%K A381679 nonn
%O A381679 0,3
%A A381679 _Seiichi Manyama_, Mar 04 2025