OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..435
FORMULA
a(n) = Sum_{m=1..n} Sum_{k=m..n} (((-1)^(k-m)+1)*(Sum_{j=m..k} binomial(j-1,m-1)*j!*2^(k-j-1)*stirling2(k,j)*(-1)^((m+k)/2+j),j,m,k))*((-1)^(n-k)+1)*Sum_{i=0..k/2} (2*i-k)^n*binomial(k,i)*(-1)^((n+k)/2-i)))/(2^k*k!))), n>0, a(0)=1.
MAPLE
a:=series(1/(1-tan(sin(x))), x=0, 23): seq(n!*coeff(a, x, n), n=0..22); # Paolo P. Lava, Mar 27 2019
MATHEMATICA
With[{nmax = 50}, CoefficientList[Series[1/(1 - Tan[Sin[x]]), {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Dec 29 2017 *)
PROG
(Maxima)
a(n):=sum(sum((((-1)^(k-m)+1)*(sum(binomial(j-1, m-1)*j!*2^(k-j-1)*stirling2(k, j)*(-1)^((m+k)/2+j), j, m, k))*((-1)^(n-k)+1)*sum((2*i-k)^n*binomial(k, i)*(-1)^((n+k)/2-i), i, 0, k/2))/(2^k*k!), k, m, n), m, 1, n);
(PARI) x='x+O('x^30); Vec(serlaplace(1/(1-tan(sin(x))))) \\ G. C. Greubel, Dec 29 2017
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( 1/(1 - Tan(Sin(x))) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Nov 07 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, May 04 2011
STATUS
approved