A143167 Second column of triangle A000369: |S2(-3;n+2,2)|.

1, 9, 111, 1785, 35595, 848925, 23586255, 748471185, 26715409875, 1059544210725, 46230843633975, 2201008238854425, 113546715232225275, 6309834090304870125, 375777507964741257375, 23876826206710426574625, 1612323634555365676819875

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: A298835 A082723 A352384 * A201532 A180788 A348068

Adjacent sequences: A143164 A143165 A143166 * A143168 A143169 A143170

Keyword

nonn,easy

Author

Wolfdieter Lang, Sep 15 2008

Status

approved