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A283120 Expansion of exp( Sum_{n>=1} sigma(8*n)*x^n/n ) in powers of x. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A027779 A073509 A198850 * A209404 A127595 A056579

Adjacent sequences:  A283117 A283118 A283119 * A283121 A283122 A283123

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Mar 01 2017

STATUS

approved

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Last modified February 27 15:59 EST 2020. Contains 332307 sequences. (Running on oeis4.)