A160710 E.g.f.: Sum_{n>=0} 2^(n^2)*log(1+x)^n/n!.

1, 2, 14, 468, 62628, 32916240, 68221619760, 561512669071200, 18431003537355665760, 2417187863502316739842560, 1267541812947815891035704645120, 2658386273978048637324643356687805440

Offset: 0

Author

Paul D. Hanna, May 25 2009

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + 2*x + 14*x^2/2! + 468*x^3/3! + 62628*x^4/4! +...
A(x) = 1 + 2*log(1+x) + 2^4*log(1+x)^2/2! + 2^9*log(1+x)^3/3! +...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..57

Crossrefs

Cf. A006025, A006024.

Programs

Mathematica

Table[Sum[StirlingS1[n, k]*2^(k^2), {k, 0, n}], {n, 0, 30}] (* G. C. Greubel, May 02 2018 *)

PARI

{a(n)=n!*polcoeff(sum(k=0,n,2^(k^2)*log(1+x+x*O(x^n))^k/k!),n)}

PARI

{a(n)=sum(k=0,n,2^(k^2)*n!*polcoeff(binomial(x, n), k))}

Formula

a(n) = Sum_{k=0..n} Stirling1(n, k)*2^(k^2) where Stirling1 numbers are described by A008275.