A306495 Expansion of e.g.f. (2-exp(-x))*exp(x)/(x-1)^2.

1, 4, 16, 74, 402, 2542, 18446, 151482, 1390738, 14126582, 157365222, 1908110866, 25022451482, 352918443438, 5327630246542, 85716034274282, 1464281837606946, 26470821156031462, 504879319309407158, 10132393298394712002, 213441590598213760042

Offset: 0

Author

Alois P. Heinz, Feb 19 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..448

Crossrefs

Row sums of A324224(n+1).

Programs

Maple

egf:= (2-exp(-x))*exp(x)/(x-1)^2:
a:= n-> n! * coeff(series(egf, x, n+1), x, n):
seq(a(n), n=0..23);
# second Maple program:
a:= proc(n) option remember; `if`(n<3, 4^n,
      (2*n+1)*a(n-1)-(n+2)*(n-1)*a(n-2)+(n-1)*(n-2)*a(n-3))
    end:
seq(a(n), n=0..23);

Formula

a(n) = Sum_{k=-n..n} A324224(n+1,k).

a(n) = (2*n+1)*a(n-1) - (n+2)*(n-1)*a(n-2) + (n-1)*(n-2)*a(n-3) for n > 2, a(n) = 4^n for n < 3.