A356029 a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/(2^k * (n - 2*k)!).

1, 1, 1, 4, 13, 61, 421, 2626, 27049, 245953, 3069721, 40222216, 576988501, 10058716669, 169773404893, 3596206855606, 73450508303761, 1775382487932001, 43993288886533489, 1183551336464017708, 34806599282992709341, 1043452963148195577181

Offset: 0

Author

Seiichi Manyama, Aug 18 2022

Keywords

• nonn

Crossrefs

Cf. A354436, A356328, A356608.

Cf. A354550, A356628, A356632.

Programs

Mathematica

a[n_] := n! * Sum[(n - 2*k)^k/(2^k*(n - 2*k)!), {k, 0, Floor[n/2]}]; a[0] = 1; Array[a, 22, 0] (* Amiram Eldar, Aug 19 2022 *)

PARI

a(n) = n!*sum(k=0, n\2, (n-2*k)^k/(2^k*(n-2*k)!));

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k*x^2/2)))))

Formula

E.g.f.: Sum_{k>=0} x^k / (k! * (1 - k*x^2/2)).