A009021 Expansion of e.g.f. cos(log(1+tan(x))).

1, 0, -1, 3, -18, 100, -726, 5698, -52028, 522720, -5849876, 71473468, -951628488, 13674233040, -211091632376, 3478906531688, -60920066577648, 1127785660994560, -21969631512312976, 448167387287730608

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..250

Mathematica

With[{nn=25}, CoefficientList[Series[Cos[Log[1+Tan[x]]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 26 2011 *)

Prog

(Maxima)
a(n):=if n=0 them 1 else sum(sum((stirling1(n-2*i, 2*m)*sum(binomial(j-1, n-2*i-1)*j!*2^(n-j)*(-1)^(n-i+j+m)*stirling2(n, j), j, n-2*i, n))/(n-2*i)!, i, 0, n/2-m), m, 0, n/2); /* Vladimir Kruchinin, Jun 20 2011 */
(PARI) x='x+O('x^30); Vec(serlaplace(cos(log(1+tan(x))))) \\ G. C. Greubel, Jul 22 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(Log(1+Tan(x))))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 22 2018

Crossrefs

Sequence in context: A180036 A038158 A327828 * A303519 A124408 A136779

Adjacent sequences: A009018 A009019 A009020 * A009022 A009023 A009024

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved