A009203 Expansion of exp(sin(tan(x))).

1, 1, 1, 2, 5, 8, 13, -232, -2199, -25600, -218311, -2258048, -20057555, -212565376, -1933691003, -21159275264, -181405779887, -1935285600256, -10159446470927, -49976214294528, 2835996855537109, 63805712413261824

Offset

0,4

Links

Table of n, a(n) for n=0..21.

Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

Formula

a(n):=sum(sum(if oddp(n+k) or oddp(k-m) then 0 else (-1)^((n+k)/2)*sum(j!*stirling2(n,j)*2^(n-j)*(-1)^(n+j-k)*binomial(j-1,k-1),j,k,n)*2^(1-m)*sum((-1)^(floor((k+m)/2)-i)*binomial(m,i)*(2*i-m)^k/k!/m!,i,0,floor(m/2)) ,k,m,n),m,1,n), n>0. - Vladimir Kruchinin, Sep 01 2010

Mathematica

With[{nn=30}, CoefficientList[Series[Exp[Sin[Tan[x]]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 13 2018 *)

Prog

(Maxima) a(n):=sum(sum(if oddp(n+k) or oddp(k-m) then 0 else (-1)^((n+k)/2)*sum(j!*stirling2(n, j)*2^(n-j)*(-1)^(n+j-k)*binomial(j-1, k-1), j, k, n)*2^(1-m)*sum((-1)^(floor((k+m)/2)-i)*binomial(m, i)*(2*i-m)^k/k!/m!, i, 0, floor(m/2)) , k, m, n), m, 1, n); /* Vladimir Kruchinin, Sep 01 2010 */

Crossrefs

Sequence in context: A200275 A075731 A009238 * A363734 A202273 A210702

Adjacent sequences: A009200 A009201 A009202 * A009204 A009205 A009206

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Prior Mathematica program replaced by Harvey P. Dale, Oct 13 2018

Status

approved