A283121 Expansion of exp( Sum_{n>=1} sigma(9*n)*x^n/n ) in powers of x.

1, 13, 104, 633, 3224, 14404, 58151, 216294, 751582, 2464860, 7689669, 22961822, 65955677, 182985947, 492016590, 1285829996, 3274100475, 8139933477, 19795490575, 47165634583, 110259083454, 253208634687, 571880965638, 1271549402110, 2785836824325, 6019078365425

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: Product_{n>=1} (1 - x^(3*n))^4/(1 - x^n)^13.

a(n) = (1/n)*Sum_{k=1..n} sigma(9*k)*a(n-k). - Seiichi Manyama, Mar 05 2017

a(n) ~ 1225 * sqrt(35) * exp(sqrt(70*n)*Pi/3) / (559872*n^3). - Vaclav Kotesovec, Mar 20 2017

Example

G.f.: A(x) = 1 + 13*x + 104*x^2 + 633*x^3 + 3224*x^4 + 14404*x^5 + ...
log(A(x)) = 13*x + 39*x^2/2 + 40*x^3/3 + 91*x^4/4 + 78*x^5/5 + 120*x^6/6 + 104*x^7/7 + 195*x^8/8 + ... + sigma(9*n)*x^n/n + ...

Crossrefs

Cf. A283123 (sigma(9*n)), A283169 (exp( Sum_{n>=1} -sigma(9*n)*x^n/n )).

Cf. A182818 (k=2), A182819 (k=3), A182820 (k=4), A182821 (k=5), A283119 (k=6), A283077 (k=7), A283120 (k=8), this sequence (k=9).

Sequence in context: A159352 A289859 A129762 * A278555 A282921 A023011

Adjacent sequences: A283118 A283119 A283120 * A283122 A283123 A283124

Keyword

nonn

Author

Seiichi Manyama, Mar 01 2017

Status

approved