A049070 - OEIS

A049070

a(n) = (n+1)^2*binomial(2*n+2,n-1)/2.

0, 2, 27, 224, 1500, 8910, 49049, 256256, 1288872, 6298500, 30093910, 141210432, 652860520, 2981331990, 13472983125, 60343756800, 268187306640, 1183875281820, 5194996380090, 22676052360000, 98513956031400, 426171522716940, 1836562780483002

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

FORMULA

G.f.: 16*x*( 2-7*x +6*x*sqrt(1-4*x) )/ ( (1-4*x)^5/2 * (1+sqrt(1-4*x))^4 ). - R. J. Mathar, Nov 19 2011

a(n) = Sum_{k=0..n} k^2 * binomial(k+n, k). - Stephen Bartell, Jul 02 2024

a(n) ~ 2^(2*n+1)*n^(3/2)/sqrt(Pi). - Stefano Spezia, Jul 10 2024

MATHEMATICA

Table[(n+1)^2 Binomial[2n+2, n-1]/2, {n, 0, 30}] (* Harvey P. Dale, Apr 15 2018 *)

PROG

(PARI) a(n) = (n+1)^2*binomial(2*n+2, n-1)/2 \\ Michel Marcus, Jun 08 2013

CROSSREFS

Sequence in context: A051766 A058406 A216087 * A197316 A175529 A267547

Adjacent sequences: A049067 A049068 A049069 * A049071 A049072 A049073

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Colin Mallows

STATUS

approved