A280939 Expansion of e.g.f.: 2*sinh(x/2) / sqrt(2 - exp(x)).

1, 1, 4, 19, 121, 946, 8779, 94249, 1148746, 15667741, 236396029, 3909054304, 70297156021, 1365847397461, 28512838809004, 636437585232559, 15125744356058821, 381337518656892106, 10164860714961807079, 285635253778131491389, 8438962752941736017146, 261512261403795336646801, 8481542634943973943517129, 287325556922319462615912544, 10148442521179099638781764121

Offset: 1

Author

Paul D. Hanna, Jan 11 2017

Keywords

• nonn

Examples

			E.g.f.: A(x) = x + x^2/2! + 4*x^3/3! + 19*x^4/4! + 121*x^5/5! + 946*x^6/6! + 8779*x^7/7! + 94249*x^8/8! + 1148746*x^9/9! + 15667741*x^10/10! + 236396029*x^11/11! + 3909054304*x^12/12! + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..250

Crossrefs

Cf. A014304, A014307.

Programs

Magma

m:=50; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(2*Sinh(x/2)/Sqrt(2 - Exp(x)))); [Factorial(n)*b[n]: n in [1..m-1]]; // G. C. Greubel, Oct 10 2018

Maple

seq(coeff(series(factorial(n)*(2*sinh(x/2)/sqrt(2-exp(x))),x,n+1), x, n), n = 1 .. 25); # Muniru A Asiru, Oct 11 2018

Mathematica

Rest[With[{nmax = 50}, CoefficientList[Series[2*Sinh[x/2]/Sqrt[2 - Exp[x]], {x, 0, nmax}], x]*Range[0, nmax]!]] (* G. C. Greubel, Oct 10 2018 *)

PARI

{a(n) = my(X=x+x*O(x^n)); n!*polcoeff( 2*sinh(X/2) / sqrt(2 - exp(X)),n)}
for(n=1,20,print1(a(n),", "))

Formula

a(n) ~ n^n / (sqrt(2) * log(2)^(n + 1/2) * exp(n)). - Vaclav Kotesovec, Jan 11 2017