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A296164 a(n) = [x^n] Product_{k>=1} ((1 + x^k)/(1 + x^(3*k)))^n. 3
1, 1, 3, 10, 35, 131, 498, 1919, 7459, 29170, 114653, 452552, 1792754, 7124040, 28386081, 113372690, 453743907, 1819317153, 7306575042, 29386858821, 118348662525, 477188876405, 1926137365804, 7782398551661, 31472648050930, 127384123318906, 515978637418884 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..500

Eric Weisstein's World of Mathematics, Schur's Partition Theorem

FORMULA

a(n) = [x^n] Product_{k>=1} 1/((1 - x^(6*k-1))*(1 - x^(6*k-5)))^n.

a(n) ~ c * d^n / sqrt(n), where d = 4.129321588075726742506... and c = 0.25764349816429874323... - Vaclav Kotesovec, May 18 2018

MATHEMATICA

Table[SeriesCoefficient[Product[((1 + x^k)/(1 + x^(3 k)))^n, {k, 1, n}], {x, 0, n}], {n, 0, 26}]

Table[SeriesCoefficient[Product[1/((1 - x^(6 k - 1)) (1 - x^(6 k - 5)))^n, {k, 1, n}], {x, 0, n}], {n, 0, 26}]

CROSSREFS

Cf. A003105, A058484, A058539, A103262, A255526, A296163.

Sequence in context: A303730 A149037 A228769 * A151046 A221130 A084781

Adjacent sequences:  A296161 A296162 A296163 * A296165 A296166 A296167

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 06 2017

STATUS

approved

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Last modified November 30 17:12 EST 2021. Contains 349424 sequences. (Running on oeis4.)