A321965 a(n) = n! [x^n] exp((1/(x - 1)^2 - 1)/2)/(1 - x).

1, 2, 8, 46, 338, 2996, 30952, 364148, 4797116, 69854968, 1113018176, 19244304872, 358608737368, 7160626365296, 152458303437728, 3446434090192816, 82412163484132112, 2077739630757428768, 55068742629150564736, 1530394053934299827168, 44490672191650220419616

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n + 3) = (n + 1)^2*(n + 2)*a(n) - (5 + 3*n)*(n + 2)*a(n + 1) + (8 + 3*n)*a(n + 2). - Robert Israel, Dec 20 2018

a(n) ~ exp(-1/3 + n^(1/3)/2 + 3*n^(2/3)/2 - n) * n^(n + 1/6) / sqrt(3). - Vaclav Kotesovec, Dec 20 2018

Maple

egf := exp((1/(x - 1)^2 - 1)/2)/(1 - x): ser := series(egf, x, 22):
seq(n!*coeff(ser, x, n), n=0..20);

Mathematica

CoefficientList[Exp[(1/(x - 1)^2 - 1)/2]/(1 - x) + O[x]^21, x] Range[0, 20]! (* Jean-François Alcover, Jan 01 2019 *)

Crossrefs

Row sums of A321966.

Sequence in context: A219358 A088791 A111552 * A229559 A128085 A052801

Adjacent sequences: A321962 A321963 A321964 * A321966 A321967 A321968

Keyword

nonn

Author

Peter Luschny, Dec 20 2018

Status

approved