A136045 Bisection of A138546.

1, 4, 42, 660, 12810, 281736, 6727644, 170316432, 4504487130, 123255492360, 3465702008340, 99645553785960, 2918768920720380, 86852063374902000, 2619552500788984200, 79939673971478231760

Offset: 0

Author

N. J. A. Sloane, Mar 25 2008

Keywords

• nonn

Programs

Maple

sq := (1-40*x+144*x^2)^(1/2); pb := 54*x*(108*x^2-27*x+1+(9*x-1)*sq);
H1 := hypergeom([7/6,1/3],[1],pb); H2 := hypergeom([1/6,4/3],[1],pb);
fa := (10-72*x-6*sq)^(1/2)/(216*x);
ogf := fa*((648*x^2+90*x+1+(54*x+3)*sq)*H1^2 - (612*x-7+3*sq)*H1*H2 + 8*(72*x-1)*H2^2); series(ogf,x=0,20); # Mark van Hoeij, Nov 12 2011

Formula

G.f.: ((41472*x^3 - 11520*x^2 + 288*x)*g'' + (-23040*x + 432 + 103680*x^2)*g' + (20736*x-864)*g)/1728 where g is the o.g.f. of A002896. - Mark van Hoeij, Nov 12 2011

a(n) = hypergeom([1/2,-n,-n],[1,2],4)*binomial(2*n,n). - Mark van Hoeij, May 13 2013

D-finite with recurrence n*(n+1)^2*a(n) +4*(-13*n^3+10*n^2+2*n-3)*a(n-1) +12*(2*n-3)*(26*n^2-61*n+39)*a(n-2) -432*(2*n-5)*(n-2)*(2*n-3)*a(n-3)=0. - R. J. Mathar, Jul 27 2022