

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*k1))*(1  x^(6*k5)))^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



