A009364 Expansion of e.g.f. log(1 + tan(sin(x))).

0, 1, -1, 3, -10, 41, -232, 1467, -11408, 100625, -1000704, 11103155, -135118080, 1795927225, -25845415936, 400540116971, -6651228620800, 117802787966241, -2216949901393920, 44174901566136419, -929133071750004736

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Mathematica

With[{nn=20}, CoefficientList[Series[Log[1+Tan[Sin[x]]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Nov 01 2021 *)

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)^(m-1), m, 1, n); /* Vladimir Kruchinin, May 05 2011 */
(PARI)
x='x+O('x^66); /* that many terms */
egf=log(1+tan(sin(x))); /* = 0 + x - 1/2*x^2 + 1/2*x^3 - 5/12*x^4 + ... */
Vec(serlaplace(egf)) /* show terms */ /* Joerg Arndt, May 05 2011 */

Crossrefs

Sequence in context: A156170 A245502 A009329 * A308951 A295236 A370537

Adjacent sequences: A009361 A009362 A009363 * A009365 A009366 A009367

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Definition corrected by Joerg Arndt, May 05 2011

Previous Mathematica program replaced by Harvey P. Dale, Nov 01 2021

Status

approved