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A217946 4^n*(n+1)*(8*n^2+32*n+33)*P(3/2,n)/(3*P(4,n)) where P(a,n) is the Pochhammer rising factorial. 1
11, 73, 387, 1876, 8670, 38907, 171171, 742456, 3186378, 13562770, 57352526, 241234488, 1010195420, 4214583135, 17527709475, 72695369520, 300782736210, 1241908383870, 5118246664410, 21058891783800, 86518038936420, 354975217564110, 1454668818567822, 5954594437631376, 24350248227272100, 99484144007729572 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Robert Israel, Table of n, a(n) for n = 0..1654

Ping Sun, Proof of two conjectures of Petkovsek and Wilf on Gessel walks Discrete Math. 312 (2012), no. 24, 3649--3655. MR2979494. See Th. 1.1, case 3.

FORMULA

From Robert Israel, Mar 28 2018: (Start)

(n+1)^2*(n+4)*(8*n^2+32*n+33)*a(n+1) = 2*(2*n+3)*(n+2)*(8*n^2+48*n+73)*a(n).

G.f.: (3-x)/(2*x^3) - (3-19*x+24*x^2-16*x^3)/(2*(1-4*x)^(3/2)*x^3). (End)

MAPLE

f:= n -> 4^n*(n+1)*(8*n^2+32*n+33)*pochhammer(3/2, n)/(3*pochhammer(4, n)):

map(f, [$0..40]); # Robert Israel, Mar 28 2018

CROSSREFS

Sequence in context: A142015 A123039 A226034 * A163775 A092244 A342830

Adjacent sequences:  A217943 A217944 A217945 * A217947 A217948 A217949

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 07 2012

STATUS

approved

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Last modified May 9 13:42 EDT 2021. Contains 343742 sequences. (Running on oeis4.)