|
%I #12 Feb 28 2017 22:35:32
%S 1,1,-1,11,-47,601,-5521,86771,-1296287,25482481,-527699041,
%T 12800059931,-335639304527,9794548687561,-308817517422961,
%U 10573293809103491,-388317397661640767,15275057087004591841,-639584224876056953281,28426125263460829489451,-1335823888802587475761007
%N E.g.f. sqrt(1+tan(2*x)).
%H Robert Israel, <a href="/A191499/b191499.txt">Table of n, a(n) for n = 0..390</a>
%F a(n) = Sum_{m=0,..,(n-1)/2} ( binomial(2*n-4*m-2,n-2*m-1)*Sum_{j=0,..,2*m} ( binomial(j+n-2*m-1,n-2*m-1)*(j+n-2*m)!*2^(6*m-n-j+1)*(-1)^(m+n+j+1)*stirling2(n,j+n-2*m)))/(n-2*m) ) ), n>0, a(0)=1.
%p S:= series(sqrt(1+tan(2*x)),x,31):
%p seq(coeff(S,x,j)*j!,j=0..30); # _Robert Israel_, Feb 28 2017
%t With[{nn = 50}, CoefficientList[Series[Sqrt[1 + Tan[2*x]], {x,0,nn}], x]*Range[0, nn]!] (* _G. C. Greubel_, Feb 28 2017 *)
%o (Maxima)
%o a(n):=sum((binomial(2*n-4*m-2,n-2*m-1)*sum(binomial(j+n-2*m-1,n-2*m-1)*(j+n-2*m)!*2^(6*m-n-j+1)*(-1)^(m+n+j+1)*stirling2(n,j+n-2*m),j,0,2*m))/(n-2*m),m,0,(n-1)/2);
%o (PARI) x='x + O('x^50); Vec(serlaplace(sqrt(1 + tan(2*x)))) \\ _G. C. Greubel_, Feb 28 2017
%K sign
%O 0,4
%A _Vladimir Kruchinin_, Jun 03 2011
|
