A370509 - OEIS

%I #14 Feb 20 2024 13:46:46

%S 1,1,2,7,28,138,818,5658,44784,399366,3962256,43289760,516432984,

%T 6679346280,93091875120,1390851720840,22175338353120,375794883339120,

%U 6745177713093840,127830886641354960,2550687440585679360,53451172032327664560,1173650135526055272960

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

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*(x*(1+x^2))^k))

%o (PARI) a(n) = sum(k=0, n\3, (n-2*k)!*binomial(n-2*k, k));

%Y Cf. A240172, A370510.

%Y Cf. A212580.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Feb 20 2024