A190123 Expansion of e.g.f.: 1/(1-tan(sin(x))).

1, 1, 2, 7, 32, 177, 1184, 9175, 81280, 810081, 8967168, 109200551, 1450641408, 20876239633, 323542851584, 5372445971063, 95157141241856, 1790769169786049, 35682993123753984, 750523142329023815, 16616642326426025984, 386288476226459349361, 9407703499451286945792

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

Sequence in context: A277359 A005362 A059439 * A006014 A121555 A265165

Adjacent sequences: A190120 A190121 A190122 * A190124 A190125 A190126

Keyword

nonn

Author

Vladimir Kruchinin, May 04 2011

Status

approved