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A298311 Expansion of Product_{k>=1} 1/((1 - x^(2*k))*(1 - x^(2*k-1))^3). 2
1, 3, 7, 16, 32, 61, 112, 197, 336, 560, 912, 1456, 2287, 3536, 5392, 8123, 12096, 17824, 26016, 37632, 53984, 76848, 108601, 152432, 212592, 294704, 406201, 556864, 759488, 1030784, 1392496, 1872784, 2508048, 3345184, 4444384, 5882747, 7758736, 10197712, 13358944, 17444256, 22708719 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of partitions of n where there are 3 kinds of odd parts.

Convolution of the sequences A000009 and A015128.

LINKS

Table of n, a(n) for n=0..40.

Index entries for related partition-counting sequences

FORMULA

G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 - x^(2*k-1))^3).

G.f.: Product_{k>=1} (1 + x^k)^2/(1 - x^k).

a(n) ~ exp(2*Pi*sqrt(n/3)) / (2^(5/2)*sqrt(3)*n). - Vaclav Kotesovec, Apr 08 2018

G.f.: 1/Product_{n > = 1} ( 1 - x^(n/gcd(n,k)) ) for k = 4. Cf. A000041 (k = 1), A015128 (k = 2), A278690 (k = 3) and A160461 (k = 5). - Peter Bala, Nov 17 2020

MATHEMATICA

nmax = 40; CoefficientList[Series[Product[1/((1 - x^(2 k)) (1 - x^(2 k - 1))^3), {k, 1, nmax}], {x, 0, nmax}], x]

nmax = 40; CoefficientList[Series[Product[(1 + x^k)^2/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A000009, A000041, A000716, A015128, A029862, A029863, A160461, A182818, A278690.

Sequence in context: A192964 A293351 A179904 * A161810 A318604 A084631

Adjacent sequences:  A298308 A298309 A298310 * A298312 A298313 A298314

KEYWORD

nonn,easy,changed

AUTHOR

Ilya Gutkovskiy, Jan 17 2018

STATUS

approved

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Last modified November 24 22:57 EST 2020. Contains 338616 sequences. (Running on oeis4.)