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

0,1

Links

Table of n, a(n) for n=0..18.

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

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 *)

Crossrefs

Sequence in context: A026090 A119751 A276475 * A318030 A018564 A004167

Adjacent sequences: A084540 A084541 A084542 * A084544 A084545 A084546

Keyword

sign,easy

Author

R. J. Mathar, Jul 01 2003

Extensions

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

Status

approved