A127016 Expansion of 1/(1+7*x*c(x)), c(x) the g.f. of Catalan numbers A000108.

1, -7, 42, -259, 1582, -9702, 59388, -363867, 2228310, -13649650, 83599852, -512063790, 3136339276, -19210260076, 117662192928, -720683271819, 4414176556902, -27036862348986, 165600668448348, -1014304512179994, 6212613590747172, -38052263986931796

Offset: 0

Author

Philippe Deléham, Mar 21 2007

Keywords

• sign

Comments

Hankel transform is (-7)^n.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Programs

Magma

R:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 2/(9 - 7*Sqrt(1-4*x)) )); // G. C. Greubel, May 31 2019

Maple

c:=(1-sqrt(1-4*x))/2/x: ser:=series(1/(1+7*x*c),x=0,25): seq(coeff(ser,x,n),n=0..22); - Emeric Deutsch, Mar 27 2007

Mathematica

CoefficientList[Series[2/(9-7*Sqrt[1-4*x]), {x,0,30}], x] (* G. C. Greubel, May 31 2019 *)

PARI

my(x='x+O('x^30)); Vec(2/(9-7*sqrt(1-4*x))) \\ G. C. Greubel, May 31 2019

Sage

(2/(9-7*sqrt(1-4*x))).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 31 2019

Formula

a(n) = Sum_{k=0..n} A039599(n,k)*(-8)^k.

G.f.: 2/(9 - 7*sqrt(1-4*x)). - G. C. Greubel, May 31 2019

D-finite with recurrence 8*n*a(n) +(17*n+48)*a(n-1) +98*(-2*n+3)*a(n-2)=0. - R. J. Mathar, Nov 22 2024

Extensions

More terms from Emeric Deutsch, Mar 27 2007