A283120 Expansion of exp( Sum_{n>=1} sigma(8*n)*x^n/n ) in powers of x.

1, 15, 128, 815, 4289, 19663, 81057, 306799, 1081986, 3594142, 11338690, 34193246, 99080387, 277046893, 750192227, 1973050940, 5053026949, 12628736331, 30859262181, 73849589786, 173333118663, 399528823032, 905418038792, 2019454523623, 4437187104779

Offset

0,2

Links

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

Formula

G.f.: Product_{n>=1} (1 - x^(2*n))^7/(1 - x^n)^15.

a(n) = (1/n)*Sum_{k=1..n} sigma(8*k)*a(n-k). - Seiichi Manyama, Mar 05 2017

a(n) ~ 529 * 23^(1/4) * exp(sqrt(23*n/3)*Pi) / (73728 * 3^(1/4) * n^(11/4)). - Vaclav Kotesovec, Mar 20 2017

Example

G.f.: A(x) = 1 + 15*x + 128*x^2 + 815*x^3 + 4289*x^4 + 19663*x^5 + ...
log(A(x)) = 15*x + 31*x^2/2 + 60*x^3/3 + 63*x^4/4 + 90*x^5/5 + 124*x^6/6 + 120*x^7/7 + 127*x^8/8 + ... + sigma(8*n)*x^n/n + ...

Crossrefs

Cf. A283122 (sigma(8*n)), A283168 (exp( Sum_{n>=1} -sigma(8*n)*x^n/n )).

Cf. A182818 (k=2), A182819 (k=3), A182820 (k=4), A182821 (k=5), A283119 (k=6), A283077 (k=7), this sequence (k=8), A283121 (k=9).

Sequence in context: A337956 A073509 A198850 * A209404 A127595 A056579

Adjacent sequences: A283117 A283118 A283119 * A283121 A283122 A283123

Keyword

nonn

Author

Seiichi Manyama, Mar 01 2017

Status

approved