A077568 a(1,n) as defined in A003148.

1, -1, 11, -39, 633, -4065, 86355, -818055, 21370545, -270059265, 8348125275, -132575387175, 4724044288425, -90632895177825, 3652562288650275, -82321915303002375, 3698358581066774625, -95898903720429434625, 4748433998702431912875, -139390494822185358126375

Offset: 0

Author

R. J. Mathar, Jul 01 2003

Keywords

• sign

Crossrefs

Cf. A003148, A084543.

Programs

Maple

A003148 := proc(m::integer,n::integer) RETURN( doublefactorial(2*n+2*m+1)/(2*m+1)*simplify(hypergeom([ -n,m+1/2],[m+3/2],2))) ; end proc:
A077568 := proc(n::integer) A003148(1,n) ; end proc:
for n from 0 to 20 do print(A077568(n)); od: # R. J. Mathar, Apr 25 2006

Mathematica

a[m_, n_] := (2n + 2m + 1)!!/(2m + 1)*Hypergeometric2F1[-n, m + 1/2, m + 3/2, 2];
Table[a[1, n], {n, 0, 15}] (* Jean-François Alcover, Jul 31 2023, after R. J. Mathar *)

Formula

Conjecture: a(n) +a(n-1) -2*(2*n+1)*(n-1)*a(n-2)=0. - R. J. Mathar, May 26 2016

Extensions

More terms from R. J. Mathar, Apr 25 2006