A277264 Expansion of Product_{k>=1} 1/(1 - x^(5*k+1)).

1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 2, 1, 1, 0, 1, 2, 2, 1, 1, 1, 3, 3, 2, 1, 2, 3, 4, 3, 2, 2, 5, 5, 5, 3, 3, 5, 8, 6, 5, 4, 7, 9, 10, 7, 6, 8, 12, 12, 11, 8, 11, 15, 17, 14, 13, 13, 19, 21, 20, 16, 19, 23, 28, 26, 23, 23, 31, 34, 35, 30, 31, 37, 46, 44, 41, 39, 48, 55, 59, 52, 52, 59, 71, 73, 71, 65, 75, 87, 94

Offset: 0

Author

Ilya Gutkovskiy, Oct 07 2016

Keywords

• nonn

Comments

Number of partitions of n into parts larger than 1 and congruent to 1 mod 5.

Examples

			a(22) = 2, because we have [16, 6] and [11, 11].
		

Links

• Index entries for related partition-counting sequences

Crossrefs

Cf. A016861, A087897, A109697 (partial sums), A117957, A277210.

Programs

Mathematica

CoefficientList[Series[(1 - x)/QPochhammer[x, x^5], {x, 0, 100}], x]

Formula

G.f.: Product_{k>=1} 1/(1 - x^(5*k+1)).

a(n) ~ Pi^(1/5) * Gamma(1/5) * exp(Pi*sqrt(2*n/15)) / (2^(21/10) * 3^(3/5) * 5^(9/10) * n^(11/10)). - Vaclav Kotesovec, Oct 09 2016