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

0,2

Links

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

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)

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 *)

Crossrefs

Cf. A005727.

Sequence in context: A150069 A150070 A150071 * A007454 A305578 A150072

Adjacent sequences: A265942 A265943 A265944 * A265946 A265947 A265948

Keyword

sign

Author

Ben Paul Thurston, Dec 23 2015

Extensions

More terms from Alois P. Heinz, Dec 23 2015

Status

approved