A190863 Expansion of 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, 1446836117077033, -112041422722084502503424

Offset

0,4

Links

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

Formula

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

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 *)

Prog

(Maxima)
a(n):=n!*sum((binomial((k)/2, (n-k)/2)*((-1)^(n-k)+1))/k!, k, 1, n)/2;
(PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(x*sqrt(1+x^2)))) /* Joerg Arndt, May 22 2011 */

Crossrefs

Sequence in context: A367326 A246145 A107462 * A022132 A041559 A339272

Adjacent sequences: A190860 A190861 A190862 * A190864 A190865 A190866

Keyword

sign

Author

Vladimir Kruchinin, May 21 2011

Status

approved