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A296162 a(n) = [x^n] Product_{k>=1} ((1 - x^(3*k))/(1 - x^k))^n. 2
1, 1, 5, 19, 89, 406, 1913, 9073, 43505, 209971, 1019390, 4971781, 24343037, 119579006, 589050663, 2908727839, 14393759457, 71360342129, 354372852011, 1762416036422, 8776797353574, 43761058841638, 218431753457637, 1091385769314272, 5458068218285909, 27319061357620056 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..25.

Eric Weisstein's World of Mathematics, Partition Function b_k

FORMULA

a(n) = [x^n] Product_{k>=1} (1 + x^k + x^(2*k))^n.

a(n) ~ c * d^n / sqrt(n), where d = 5.1069752682291604222843644516987970799026747758649349... and c = 0.271879273312907861082536692355942116774864... - Vaclav Kotesovec, May 13 2018

MATHEMATICA

Table[SeriesCoefficient[Product[((1 - x^(3 k))/(1 - x^k))^n, {k, 1, n}], {x, 0, n}], {n, 0, 25}]

Table[SeriesCoefficient[Product[(1 + x^k + x^(2 k))^n, {k, 1, n}], {x, 0, n}], {n, 0, 25}]

CROSSREFS

Cf. A000726, A008485, A121596, A128758, A270913, A285927, A296044, A296163.

Sequence in context: A149804 A340994 A301702 * A144036 A110210 A244899

Adjacent sequences:  A296159 A296160 A296161 * A296163 A296164 A296165

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 06 2017

STATUS

approved

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Last modified April 11 12:38 EDT 2021. Contains 342886 sequences. (Running on oeis4.)