A370509 Expansion of Sum_{k>=0} k! * ( x * (1+x^2) )^k.

1, 1, 2, 7, 28, 138, 818, 5658, 44784, 399366, 3962256, 43289760, 516432984, 6679346280, 93091875120, 1390851720840, 22175338353120, 375794883339120, 6745177713093840, 127830886641354960, 2550687440585679360, 53451172032327664560, 1173650135526055272960

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = Sum_{k=0..floor(n/3)} (n-2*k)! * binomial(n-2*k,k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*(x*(1+x^2))^k))
(PARI) a(n) = sum(k=0, n\3, (n-2*k)!*binomial(n-2*k, k));

Crossrefs

Cf. A240172, A370510.

Cf. A212580.

Sequence in context: A297195 A116539 A266467 * A141318 A276080 A352659

Adjacent sequences: A370506 A370507 A370508 * A370510 A370511 A370512

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 20 2024

Status

approved