A381680 Euler transform of A115224.
1, 1, 29, 263, 1565, 11217, 74412, 482638, 2987123, 18066149, 107415185, 623612637, 3552605428, 19882256022, 109518424910, 594290145192, 3179607733480, 16790129919934, 87573088547032, 451477766533886, 2302069862201553, 11616226357007259, 58036597014533469
Offset: 0
Keywords
Programs
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Mathematica
a[0] = 1; a[n_] := a[n] = Sum[DivisorSigma[6, k^2]/DivisorSigma[3, k^2]*a[n-k], {k, 1, n}]/n; Table[a[n], {n, 0, 30}] (* Vaclav Kotesovec, Mar 04 2025 *) -
PARI
my(N=30, x='x+O('x^N)); Vec(exp(sum(k=1, N, sigma(k^2, 6)/sigma(k^2, 3)*x^k/k)))
Formula
G.f.: 1/Product_{k>=1} (1 - x^k)^A115224(k).
G.f.: exp( Sum_{k>=1} sigma_6(k^2)/sigma_3(k^2) * x^k/k ).
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} sigma_6(k^2)/sigma_3(k^2) * a(n-k).
log(a(n)) ~ 7 * 5^(2/7) * zeta(7)^(1/7) * n^(6/7) / (2^(2/7) * 3^(3/7) * Pi^(4/7)). - Vaclav Kotesovec, Mar 04 2025