A277958 Expansion of Product_{n>=1} (1 - x^(7*n))^7/(1 - x^n)^8 in powers of x.

1, 8, 44, 192, 726, 2464, 7704, 22521, 62281, 164252, 415796, 1015334, 2401462, 5519640, 12363062, 27047913, 57917068, 121588588, 250638216, 507974950, 1013409244, 1992161935, 3862461694, 7392045512, 13975011909, 26116935550, 48277368020, 88320521108, 159993054081

Offset: 0

Author

Seiichi Manyama, Nov 06 2016

Keywords

• nonn

Examples

			G.f.: 1 + 8*x + 44*x^2 + 192*x^3 + 726*x^4 + 2464*x^5 + 7704*x^6 + ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Wikipedia, Ramanujan's congruences

Crossrefs

Cf. A071746, A160527, A213261.

Programs

Mathematica

nmax = 20; CoefficientList[Series[Product[(1 - x^(7*k))^7 /(1 - x^k)^8 , {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *)

Formula

G.f.: Product_{n>=1} (1 - x^(7*n))^7/(1 - x^n)^8.

A213261(n) = 7*A160527(n) + 49*a(n - 1) for n > 0 due to Ramanujan's congruences.

a(n) ~ exp(Pi*sqrt(98*n/21)) / (1372*sqrt(3)*n). - Vaclav Kotesovec, Nov 10 2017