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URL: https://oeis.org/A009364

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A009364
Expansion of e.g.f. log(1 + tan(sin(x))).
0
0, 1, -1, 3, -10, 41, -232, 1467, -11408, 100625, -1000704, 11103155, -135118080, 1795927225, -25845415936, 400540116971, -6651228620800, 117802787966241, -2216949901393920, 44174901566136419, -929133071750004736
OFFSET
0,4
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 * A393400 A308951 A295236
KEYWORD
sign,easy
AUTHOR
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