OFFSET
0,3
FORMULA
a(n) = (-1)^n * n! * Sum_{k=0..n} binomial(2*k-1,n-k)/k!.
D-finite with recurrence a(n) +(-n+1)*a(n-1) +5*(-n+1)*a(n-2) +7*(n-1)*(n-2)*a(n-3) -3*(n-1)*(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Aug 14 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-x)^2)/(1-x)))
(PARI) a(n) = (-1)^n*n!*sum(k=0, n, binomial(2*k-1, n-k)/k!);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Aug 14 2024
STATUS
approved