cp's OEIS Frontend

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.

A307816 a(1) = 1; a(n) = Sum_{k=1..n-1} a(n-k) * Sum_{d|k} a(d)*a(k/d).

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%I A307816 #7 Apr 30 2019 21:49:46
%S A307816 1,1,3,11,46,201,928,4399,21431,106399,536896,2744532,14185314,
%T A307816 73999955,389131156,2060478226,10976863244,58792036053,316397505099,
%U A307816 1710037259744,9277953713444,50514377326158,275903656802218,1511334791637679,8300811367229306,45703063861360901
%N A307816 a(1) = 1; a(n) = Sum_{k=1..n-1} a(n-k) * Sum_{d|k} a(d)*a(k/d).
%F A307816 G.f.: A(x) = Sum_{n>=1} a(n)*x^n = x + (Sum_{n>=1} a(n)*x^n) * (Sum_{i>=1} Sum_{j>=1} a(i)*a(j)*x^(i*j)).
%t A307816 a[n_] := a[n] = Sum[a[n - k] Sum[a[d] a[k/d], {d, Divisors[k]}], {k, 1, n - 1}]; a[1] = 1; Table[a[n], {n, 1, 26}]
%t A307816 a[n_] := a[n] = SeriesCoefficient[x + Sum[a[k] x^k, {k, 1, n - 1}]  Sum[Sum[a[i] a[j] x^(i j), {j, 1, n - 1}], {i, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 26}]
%o A307816 (PARI) lista(nn) = { my(va=vector(nn)); va[1] = 1; for (n=2, nn, va[n] = sum(k=1, n-1, va[n-k] * sumdiv(k, d, va[d]*va[k/d]))); va;} \\ _Michel Marcus_, Apr 30 2019
%Y A307816 Cf. A038044, A317875.
%K A307816 nonn
%O A307816 1,3
%A A307816 _Ilya Gutkovskiy_, Apr 30 2019