A190863 E.g.f. exp(x*sqrt(1+x^2)).

1, 1, 1, 4, 13, 16, 61, 736, 1849, -12032, 15481, 1386496, 737221, -139053056, 8889973, 22783492096, 577232881, -4931048505344, 9090479089, 1391155770032128, 747609240061, -492982133885763584, 14533568173741, 214285634326006595584

Offset: 0

Author

Vladimir Kruchinin, May 21 2011

Keywords

• sign

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..105

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[x Sqrt[1+x^2]],{x,0,nn}],x]Range[0,nn]!] (* Harvey P. Dale, Mar 23 2013 *)

Maxima

a(n):=n!*sum((binomial((k)/2,(n-k)/2)*((-1)^(n-k)+1))/k!,k,1,n)/2;

PARI

x='x+O('x^66); /* that many terms */
Vec(serlaplace(exp(x*sqrt(1+x^2)))) /* show terms */ /* Joerg Arndt, May 22 2011 */

Formula

a(n)=n!*sum(k=1..n, (binomial(k/2,(n-k)/2)*((-1)^(n-k)+1))/k!)/2.