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

Author

Seiichi Manyama, Feb 20 2024

Keywords

• nonn
• easy

Crossrefs

Cf. A240172, A370510.

Cf. A212580.

Programs

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));

Formula

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