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A270995 Expansion of Product_{k>=1} 1/(1 - A000009(k)*x^k). 6
1, 1, 2, 4, 7, 12, 23, 37, 64, 108, 180, 290, 488, 772, 1251, 2001, 3180, 4982, 7913, 12261, 19162, 29669, 45804, 70187, 108029, 164276, 250267, 379439, 574067, 864044, 1302169, 1949050, 2917900, 4352796, 6481627, 9620256, 14274080, 21090608, 31142909 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The number of ways a number can be partitioned into not necessarily distinct parts and then each part is partitioned into distinct parts. Also a(n) > A089259(n) for n>5. - Gus Wiseman, Apr 10 2016

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

Vaclav Kotesovec, Graph - The asymptotic ratio (100000 terms)

FORMULA

From Vaclav Kotesovec, Mar 28 2016: (Start)

a(n) ~ c * n^2 * 2^(n/3), where

c = 436246966131366188.9451742926272200575837456478739... if mod(n,3) = 0

c = 436246966131366188.9351143199611598469443841182807... if mod(n,3) = 1

c = 436246966131366188.9322714926383227135786894927498... if mod(n,3) = 2

(End)

EXAMPLE

a(6)=23: {(6), (5)(1), (51), (4)(2), (42), (4)(1)(1), (41)(1), (3)(3), (3)(2)(1), (3)(21), (32)(1), (31)(2), (21)(3), (321), (3)(1)(1)(1), (31)(1)(1), (2)(2)(2), (2)(2)(1)(1), (21)(2)(1), (21)(21), (2)(1)(1)(1)(1), (21)(1)(1)(1), (1)(1)(1)(1)(1)(1)}.

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[1/(1-PartitionsQ[k]*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A063834 (twice partitioned numbers), A089259, A271619.

Sequence in context: A280352 A135360 A082548 * A007323 A099604 A026790

Adjacent sequences:  A270992 A270993 A270994 * A270996 A270997 A270998

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 28 2016

STATUS

approved

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Last modified December 11 05:41 EST 2017. Contains 295868 sequences.