A281461 Expansion of Product_{k>=1} (1 + x^(7*k-3))*(1 + x^(7*k-4)).

1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 2, 1, 0, 2, 2, 0, 1, 3, 1, 0, 3, 3, 0, 2, 5, 2, 1, 5, 5, 1, 3, 7, 3, 1, 7, 7, 1, 5, 11, 5, 2, 11, 11, 2, 7, 15, 7, 3, 15, 15, 4, 11, 22, 11, 6, 22, 22, 6, 15, 30, 15, 8, 30, 30, 9, 22, 42, 22, 13, 42, 42, 14, 30, 56

Offset: 0

Author

Vaclav Kotesovec, Jan 22 2017

Keywords

• nonn

Comments

Convolution of A281456 and A281457.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A035435, A281456, A281457.

Programs

Mathematica

nmax = 100; CoefficientList[Series[Product[(1 + x^(7*k-3))*(1 + x^(7*k-4)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ exp(sqrt(2*n/21)*Pi) / (2^(5/4)*21^(1/4)*n^(3/4)) * (1 - (3*sqrt(21/2)/(8*Pi) + 23*Pi/(84*sqrt(42))) / sqrt(n)). - Vaclav Kotesovec, Jan 22 2017, extended Jan 24 2017