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A143167 Second column of triangle A000369: |S2(-3;n+2,2)|. 2
1, 9, 111, 1785, 35595, 848925, 23586255, 748471185, 26715409875, 1059544210725, 46230843633975, 2201008238854425, 113546715232225275, 6309834090304870125, 375777507964741257375, 23876826206710426574625, 1612323634555365676819875 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Robert Israel, Table of n, a(n) for n = 0..364

FORMULA

a(n) = A000369(n+2,2) = |S2(-3;n+2,2)|, n >= 0.

E.g.f.: d^2/dx^2 ((1-(1-4*x)^(1/4))^2 )/2! = (3 - 2*(1-4*x)^(1/4))/(1-4*x)^(7/4).

From Robert Israel, Jan 09 2019: (Start)

a(n) = (8*n+1)*a(n-1) - 2*(4*n-1)*(2*n-1)*a(n-2).

a(n) = 4^(n+1)*(Gamma(n+7/4)/Gamma(3/4) - Gamma(n+3/2)/Gamma(1/2)). (End)

MAPLE

f:= gfun:-rectoproc({a(n) = (8*n+1)*a(n-1) - 2*(4*n-1)*(2*n-1)*a(n-2), a(0)=1, a(1)=9}, a(n), remember):

map(f, [$0..50]); # Robert Israel, Jan 09 2019

PROG

(PARI) x = 'x + O('x^40); serlaplace((3 - 2*(1-4*x)^(1/4))/(1-4*x)^(7/4)) \\ Michel Marcus, Jun 18 2017

CROSSREFS

First column of A000369 is A008545, third one is A143168.

Sequence in context: A058607 A298835 A082723 * A201532 A180788 A241804

Adjacent sequences:  A143164 A143165 A143166 * A143168 A143169 A143170

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Sep 15 2008

STATUS

approved

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Last modified June 16 07:14 EDT 2019. Contains 324145 sequences. (Running on oeis4.)