A009623 Expansion of e.g.f. sinh(x)*exp(sinh(x)).

0, 1, 2, 4, 12, 36, 118, 456, 1816, 7888, 37354, 184064, 974372, 5444544, 31769182, 195982208, 1259350576, 8441139456, 59073098706, 428299217920, 3226127944764, 25165446157312, 202778723085382, 1689266143553536, 14503292667068744, 128288107134734336, 1168138817072817594

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Formula

a(n) = D^n(x*exp(x)) evaluated at x = 0, where D is the operator sqrt(1+x^2)*d/dx. Cf. A003724 and A009541. - Peter Bala, Dec 06 2011

Mathematica

With[{nn=30}, CoefficientList[Series[Sinh[x]*Exp[Sinh[x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jun 07 2022 *)

Crossrefs

Cf. A003724, A009541.

Sequence in context: A054542 A214198 A117757 * A148208 A245798 A241530

Adjacent sequences: A009620 A009621 A009622 * A009624 A009625 A009626

Keyword

nonn,easy

Author

R. H. Hardin

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997

Previous Mathematica program replaced by Harvey P. Dale, Jun 07 2022

More terms from Jason Yuen, Sep 21 2025

Status

approved