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%I #14 Sep 08 2022 08:46:18
%S 1,1,4,19,121,946,8779,94249,1148746,15667741,236396029,3909054304,
%T 70297156021,1365847397461,28512838809004,636437585232559,
%U 15125744356058821,381337518656892106,10164860714961807079,285635253778131491389,8438962752941736017146,261512261403795336646801,8481542634943973943517129,287325556922319462615912544,10148442521179099638781764121
%N Expansion of e.g.f.: 2*sinh(x/2) / sqrt(2 - exp(x)).
%H G. C. Greubel, <a href="/A280939/b280939.txt">Table of n, a(n) for n = 1..250</a>
%F a(n) ~ n^n / (sqrt(2) * log(2)^(n + 1/2) * exp(n)). - _Vaclav Kotesovec_, Jan 11 2017
%e 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! + ...
%p 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
%t 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 *)
%o (PARI) {a(n) = my(X=x+x*O(x^n)); n!*polcoeff( 2*sinh(X/2) / sqrt(2 - exp(X)),n)}
%o for(n=1,20,print1(a(n),", "))
%o (Magma) m:=50; R<x>:=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
%Y Cf. A014304, A014307.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Jan 11 2017
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