login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A052603
E.g.f. (1-x)^3/(1-4x+3x^2-x^3).
0
1, 1, 8, 78, 984, 15480, 292320, 6441120, 162207360, 4595512320, 144662112000, 5009199148800, 189221439052800, 7743449813299200, 341258374762905600, 16113703632009984000, 811588993992032256000, 43431603596770701312000
OFFSET
0,3
FORMULA
E.g.f.: (-1+x)^3/(-1+4*x-3*x^2+x^3)
Recurrence: {a(1)=1, a(0)=1, a(2)=8, (-11*n-6-n^3-6*n^2)*a(n)+(18+3*n^2+15*n)*a(n+1)+(-4*n-12)*a(n+2)+a(n+3)=0, a(3)=78}
Sum(-1/31*(5*_alpha+3*_alpha^2-6)*_alpha^(-1-n), _alpha=RootOf(-1+4*_Z-3*_Z^2+_Z^3))*n!
a(n)=n!*A052529(n). - R. J. Mathar, Jun 03 2022
MAPLE
spec := [S, {S=Sequence(Prod(Z, Sequence(Z), Sequence(Z), Sequence(Z)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
CROSSREFS
Sequence in context: A058480 A000435 A052698 * A071556 A316203 A303507
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved