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.

A329803 a(1) = 1; a(n) = Sum_{d|n, d < n} q(n/d) * a(d), where q() = A000009.

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%I A329803 #4 Nov 21 2019 22:16:24
%S A329803 1,1,2,3,3,8,5,11,12,16,12,37,18,32,39,55,38,90,54,105,96,113,104,236,
%T A329803 151,201,232,301,256,450,340,517,496,588,615,988,760,972,1054,1395,
%U A329803 1260,1766,1610,2078,2240,2512,2590,3653,3289,4029,4249,5038,5120,6526
%N A329803 a(1) = 1; a(n) = Sum_{d|n, d < n} q(n/d) * a(d), where q() = A000009.
%F A329803 G.f. A(x) satisfies: A(x) = x + Sum_{k>=2} q(k) * A(x^k).
%t A329803 a[n_] := If[n == 1, n, Sum[If[d < n, PartitionsQ[n/d] a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 54}]
%t A329803 nmax = 54; A[_] = 0; Do[A[x_] = x + Sum[PartitionsQ[k] A[x^k], {k, 2, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
%Y A329803 Cf. A000009, A050354, A050369, A074206, A308076, A328424.
%K A329803 nonn
%O A329803 1,3
%A A329803 _Ilya Gutkovskiy_, Nov 21 2019