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A283077 Expansion of Product_{n>=1} (1 - x^(7*n))/(1 - x^n)^8 in powers of x. 5
1, 8, 44, 192, 726, 2464, 7704, 22527, 62329, 164516, 416948, 1019690, 2416246, 5565864, 12498215, 27421815, 58903768, 124088548, 256749822, 522450250, 1046735092, 2066948472, 4026431543, 7743987036, 14715788745, 27648250012, 51390298666, 94550761844 (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.: exp( Sum_{n>=1} sigma(7*n)*x^n/n ).

a(n) = (1/n)*Sum_{k=1..n} sigma(7*k)*a(n-k). - Seiichi Manyama, Mar 05 2017

a(n) ~ 3025 * exp(sqrt(110*n/21)*Pi) / (28224*sqrt(14)*n^(5/2)). - Vaclav Kotesovec, Mar 20 2017

EXAMPLE

G.f.: A(x) = 1 + 8*x + 44*x^2 + 192*x^3 + 726*x^4 + 2464*x^5 + ...

log(A(x)) = 8*x + 24*x^2/2 + 32*x^3/3 + 56*x^4/4 + 48*x^5/5 + 96*x^6/6 + 57*x^7/7 + 120*x^8/8 + ... + sigma(7*n)*x^n/n + ...

CROSSREFS

Cf. A282942 (Product_{n>=1} (1 - x^n)^8/(1 - x^(7*n))), A283078 (sigma(7*n)).

Cf. exp( Sum_{n>=1} sigma(k*n)*x^n/n ): A182818 (k=2), A182819 (k=3), A182820 (k=4), A182821 (k=5), A283119 (k=6), this sequence (k=7), A283120 (k=8), A283121 (k=9).

Sequence in context: A092877 A160521 A277958 * A023007 A169795 A073380

Adjacent sequences:  A283074 A283075 A283076 * A283078 A283079 A283080

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Feb 28 2017

STATUS

approved

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Last modified January 25 16:42 EST 2020. Contains 331245 sequences. (Running on oeis4.)