A009585 E.g.f. sinh(log(1+x)^2).

0, 0, 2, -6, 22, -100, 668, -6048, 64776, -763488, 9676152, -131167080, 1900043880, -29387788560, 484545133200, -8496674716320, 158018410132800, -3107703909004800, 64445168622156960, -1405303346393768160

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..445

Formula

a(n) = Sum_{j=1..(n+1)/2} (4*j-2)!/(2*j-1)!*stirling1(n,4*j-2)), n>0, a(0) = 0. - Vladimir Kruchinin, Jun 08 2011

Example

sinh(log(x+1)^2) = 2/2!*x^2-6/3!*x^3+22/4!*x^4-100/5!*x^5...

Mathematica

With[{nmax = 50}, CoefficientList[Series[Sinh[Log[1 + x]^2], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jan 22 2018 *)

Prog

(Maxima) a(n):=sum((4*j-2)!/(2*j-1)!*stirling1(n, 4*j-2), j, 1, (n+1)/2); /* Vladimir Kruchinin, Jun 08 2011 */
(PARI) x='x+O('x^30); concat([0], Vec(serlaplace(sinh(log(1+x)^2)))) \\ G. C. Greubel, Jan 22 2018

Crossrefs

Sequence in context: A052517 A245119 A012270 * A012267 A012268 A009655

Adjacent sequences: A009582 A009583 A009584 * A009586 A009587 A009588

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved