A277958 - OEIS

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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

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OFFSET

0,2

LINKS

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

Wikipedia, Ramanujan's congruences

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

EXAMPLE

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