A265945 n-th derivative of x^(2*x) at x=1.

1, 2, 6, 18, 64, 220, 888, 3192, 15104, 48096, 338400, 285120, 13728768, -75484032, 1327431168, -15621137280, 232048220160, -3468200017920, 56208508250112, -959557688285184, 17344153658234880, -330228975428997120, 6611419866845122560, -138844103855232061440

Offset: 0

Author

Ben Paul Thurston, Dec 23 2015

Keywords

• sign

Links

• Robert Israel, Table of n, a(n) for n = 0..450

Crossrefs

Cf. A005727.

Programs

Maple

S:= series((x+1)^(2*x+2), x, 51):
seq(coeff(S,x,j)*j!, j=0..50); # Robert Israel, Dec 23 2015

Mathematica

With[{nn=30},CoefficientList[Series[(x+1)^(2x+2),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 20 2018 *)

Formula

E.g.f.: (x+1)^(2*x+2).

From Robert Israel, Dec 23 2015: (Start)

a(n) = Sum_{k=0..n} binomial(n,j)*A005727(j)*A005727(n-j).

a(n+1) = 2*(a(n) + Sum_{k=0..n-1} (-1)^(n-1-k)*n!*a(k)/((n-k)*k!)). (End)

Extensions

More terms from Alois P. Heinz, Dec 23 2015