A009061 Expansion of e.g.f. cos(sinh(x)*exp(x)).

1, 0, -1, -6, -27, -100, -237, 742, 18025, 194904, 1689671, 12483570, 72272013, 155614004, -4305757029, -101460169442, -1561477983407, -20064006763728, -223375429298929, -2048612121431958, -11401251676320843, 95849085744834380

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250
• Eric Weisstein's MathWorld, Bell Polynomial.

Crossrefs

Cf. A009496, A121868.

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(Sinh(x)*Exp(x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 23 2018

Maple

seq(coeff(series(factorial(n)*cos(sinh(x)*exp(x)), x,n+1),x,n),n=0..25); # Muniru A Asiru, Jul 24 2018

Mathematica

Table[SeriesCoefficient[Cos[Sinh[x] Exp[x]], {x, 0, n}] n!, {n, 0, 20}]
Table[2^n Re[BellB[n, I/2]], {n, 0, 20}] (* Vladimir Reshetnikov, Oct 22 2015 *)

PARI

x='x+O('x^30); Vec(serlaplace(cos(sinh(x)*exp(x)))) \\ G. C. Greubel, Jul 23 2018

Formula

a(n) = 2^n*Re(B_n(i/2)), where B_n(x) is n-th Bell polynomial, i=sqrt(-1). Vladimir Reshetnikov, Oct 22 2015

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997