A191499 E.g.f. sqrt(1+tan(2*x)).

1, 1, -1, 11, -47, 601, -5521, 86771, -1296287, 25482481, -527699041, 12800059931, -335639304527, 9794548687561, -308817517422961, 10573293809103491, -388317397661640767, 15275057087004591841, -639584224876056953281, 28426125263460829489451, -1335823888802587475761007

Offset

0,4

Links

Robert Israel, Table of n, a(n) for n = 0..390

Formula

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.

Maple

S:= series(sqrt(1+tan(2*x)), x, 31):
seq(coeff(S, x, j)*j!, j=0..30); # Robert Israel, Feb 28 2017

Mathematica

With[{nn = 50}, CoefficientList[Series[Sqrt[1 + Tan[2*x]], {x, 0, nn}], x]*Range[0, nn]!] (* G. C. Greubel, Feb 28 2017 *)

Prog

(Maxima)
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);
(PARI) x='x + O('x^50); Vec(serlaplace(sqrt(1 + tan(2*x)))) \\ G. C. Greubel, Feb 28 2017

Crossrefs

Sequence in context: A354590 A067355 A138362 * A072372 A230982 A024530

Adjacent sequences: A191496 A191497 A191498 * A191500 A191501 A191502

Keyword

sign

Author

Vladimir Kruchinin, Jun 03 2011

Status

approved