A277210 -id:A277210 - cp's OEIS frontend

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

Ilya Gutkovskiy, Oct 07 2016

nonn

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

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

Index entries for related partition-counting sequences

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

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

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

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

Original entry on oeis.org

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

Ilya Gutkovskiy, Oct 10 2016

nonn

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

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

Robert Israel, Table of n, a(n) for n = 0..3000
Index entries for related partition-counting sequences

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

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

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

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

cp's OEIS Frontend

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

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