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A306495 Expansion of e.g.f. (2-exp(-x))*exp(x)/(x-1)^2. 2
1, 4, 16, 74, 402, 2542, 18446, 151482, 1390738, 14126582, 157365222, 1908110866, 25022451482, 352918443438, 5327630246542, 85716034274282, 1464281837606946, 26470821156031462, 504879319309407158, 10132393298394712002, 213441590598213760042 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

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.

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);

CROSSREFS

Row sums of A324224(n+1).

Sequence in context: A301455 A214372 A109957 * A331159 A101205 A301577

Adjacent sequences: A306492 A306493 A306494 * A306496 A306497 A306498

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 19 2019

STATUS

approved

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Last modified December 8 08:22 EST 2022. Contains 358693 sequences. (Running on oeis4.)