A084543 a(2,n) as defined in A003148.

3, -9, 69, -531, 6147, -73665, 1143045, -18456795, 359420355, -7279744185, 170639259525, -4151789871075, 113815089771075, -3231091019581425, 101428235414230725, -3289812808335928875, 116369085609950047875, -4244245621899589931625, 167038144384492533277125

Offset: 0

Author

R. J. Mathar, Jul 01 2003

Keywords

• sign
• easy

Programs

Maple

A003148 := proc(m::integer,n::integer) doublefactorial(2*n+2*m+1)/(2*m+1)*simplify(hypergeom([ -n,m+1/2],[m+3/2],2)) ; end proc:
A084543 := proc(n::integer) A003148(2,n) ; end proc:
seq(A084543(n),n=0..40) : # 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[2, n], {n, 0, 20}] (* Jean-François Alcover, Jul 31 2023, after R. J. Mathar *)

Formula

D-finite with recurrence a(n) + 3*a(n-1) - 2*(2*n+3)*(n-1)*a(n-2) = 0. - R. J. Mathar, Mar 12 2013

Extensions

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