A283077 Expansion of Product_{n>=1} (1 - x^(7*n))/(1 - x^n)^8 in powers of x.

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

Offset: 0

Author

Seiichi Manyama, Feb 28 2017

Keywords

• nonn

Examples

			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 + ...
		

Links

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

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).

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