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 A191688 E.g.f. 1/(1-sin(x)^3) 0

%I

%S 1,0,0,6,0,-60,720,546,-40320,357960,1693440,-59830914,414120960,

%T 6693648780,-171958026240,666035353626,40363372707840,

%U -832144532031600,-1304413871800320,365125143426482166,-5976042240729415680

%N E.g.f. 1/(1-sin(x)^3)

%F a(n)=sum(k=1..n, (((-1)^(n-3*k)+1)*sum(i=0..(3*k)/2, (2*i-3*k)^n*binomial(3*k,i)*(-1)^((n+3*k)/2-i)))/2^(3*k)), n>0, a(0)=1.

%t With[{nn=30},CoefficientList[Series[1/(1-Sin[x]^3),{x,0,nn}],x] Range[ 0,nn]!] (* From Harvey P. Dale, Oct 11 2011 *)

%o (Maxima)

%o a(n):=sum((((-1)^(n-3*k)+1)*sum((2*i-3*k)^n*binomial(3*k,i)*(-1)^((n+3*k)/2-i),i,0,(3*k)/2))/2^(3*k),k,1,n);

%K sign

%O 0,4

%A _Vladimir Kruchinin_, Jun 11 2011

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