A277349 Expansion of Product_{k>=1} 1/(1 - x^(6*k+1)).

1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 2, 1, 1, 0, 0, 1, 2, 2, 1, 1, 0, 1, 3, 3, 2, 1, 1, 1, 3, 4, 3, 2, 1, 2, 4, 5, 5, 3, 2, 2, 5, 7, 6, 5, 3, 3, 6, 9, 9, 7, 5, 4, 7, 11, 12, 10, 7, 6, 9, 14, 16, 14, 11, 8, 11, 17, 20, 19, 15, 12, 14, 21, 26, 25, 21, 17, 18, 26, 32, 33, 28, 23, 24, 32, 41

Offset

0,27

Comments

Number of partitions of n into parts larger than 1 and congruent to 1 mod 6.

Links

Robert Israel, Table of n, a(n) for n = 0..3000

Index entries for related partition-counting sequences

Formula

G.f.: Product_{k>=1} 1/(1 - x^(6*k+1)).

a(n) ~ Pi^(1/6) * Gamma(1/6) * exp(sqrt(n)*Pi/3) / (24*sqrt(3)*n^(13/12)). - Vaclav Kotesovec, Oct 10 2016

Example

a(26) = 2, because we have [19, 7] and [13, 13].

Maple

N:= 100:
G:= 1/mul(1-x^m, m=7..N, 6):
S:= series(G, x, N+1):
seq(coeff(S, x, j), j=0..N); # Robert Israel, Jan 23 2019

Mathematica

CoefficientList[Series[(1 - x)/QPochhammer[x, x^6], {x, 0, 100}], x]

Crossrefs

Cf. A016921, A087897, A109701 (partial sums), A117957, A277210, A277264.

Sequence in context: A113447 A137608 A191336 * A078807 A208249 A329985

Adjacent sequences: A277346 A277347 A277348 * A277350 A277351 A277352

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 10 2016

Status

approved