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A245551 G.f.: 1/(1-2*x-3*x^2)^(5/2). 1
1, 5, 25, 105, 420, 1596, 5880, 21120, 74415, 258115, 883883, 2994355, 10051860, 33479460, 110750580, 364177332, 1191186855, 3877914915, 12571302975, 40598200335, 130657125984, 419173385400, 1340928798300, 4278305877300, 13617034683525, 43243221276801, 137040737988105 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

J. Y. X. Yang, M. X. X. Zhong, R. D. P. Zhou, On the Enumeration of (s, s+ 1, s+2)-Core Partitions, arXiv preprint arXiv:1406.2583 [math.CO], 2014. See Theorem 4.2.

FORMULA

a(n) ~ 3^(n+3/2) * n^(3/2) / (8*sqrt(Pi)). - Vaclav Kotesovec, Jul 31 2014

a(n) = (2+3/n)*a(n-1) + (3+9/n)*a(n-2) for n >= 2. - Robert Israel, Aug 01 2014

MAPLE

A[0]:= 1: A[1]:= 5:

for n from 2 to 100 do

A[n]:= (2+3/n)*A[n-1] + (3+9/n)*A[n-2]

od:

seq(A[n], n=0..100); # Robert Israel, Aug 01 2014

MATHEMATICA

CoefficientList[Series[1/(1 - 2 x - 3 x^2)^(5/2), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 01 2014 *)

PROG

(PARI) x='x+O('x^50); Vec(1/(1-2*x-3*x^2)^(5/2)) \\ G. C. Greubel, Apr 06 2017

CROSSREFS

Sequence in context: A293885 A209836 A272762 * A146882 A218264 A264018

Adjacent sequences:  A245548 A245549 A245550 * A245552 A245553 A245554

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 30 2014

STATUS

approved

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Last modified January 28 13:11 EST 2020. Contains 331321 sequences. (Running on oeis4.)