A308400 Expansion of 1 / Sum_{k=-oo..oo} (-x)^(k*(6*k + 1)).

1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 1, 0, 3, 0, 3, 1, 1, 3, 0, 6, 1, 3, 3, 1, 8, 1, 8, 3, 3, 9, 2, 14, 3, 9, 9, 4, 19, 4, 19, 9, 10, 21, 6, 32, 10, 22, 22, 12, 42, 12, 43, 23, 25, 48, 18, 67, 25, 51, 51, 31, 88, 31, 90, 54, 59, 101, 44, 137, 60, 108, 109, 73, 177, 73

Offset

0,13

Comments

Number of partitions of n into parts congruent to {0, 5, 7} mod 12.

Convolution inverse of A247223.

Links

Table of n, a(n) for n=0..78.

Formula

G.f.: 1 / Sum_{k>=1} (-x)^A036498(k).

G.f.: Product_{k>=1} 1 / ((1 - x^(12*k - 7)) * (1 - x^(12*k - 5)) * (1 - x^(12*k))).

a(n) ~ (sqrt(3) - 1) * exp(sqrt(n/6)*Pi) / (2^(5/2)*n). - Vaclav Kotesovec, May 25 2019

Mathematica

nmax = 78; CoefficientList[Series[1/Sum[(-x)^(k (6 k + 1)), {k, -nmax, nmax}], {x, 0, nmax}], x]
nmax = 78; CoefficientList[Series[Product[1/((1 - x^(12 k - 7)) * (1 - x^(12 k - 5)) * (1 - x^(12 k))), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A006950, A036498, A049453, A210964, A247223, A263536, A308399.

Sequence in context: A036851 A036850 A260492 * A369816 A236541 A113206

Adjacent sequences: A308397 A308398 A308399 * A308401 A308402 A308403

Keyword

nonn

Author

Ilya Gutkovskiy, May 24 2019

Status

approved