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A009203 Expansion of exp(sin(tan(x))). 3
1, 1, 1, 2, 5, 8, 13, -232, -2199, -25600, -218311, -2258048, -20057555, -212565376, -1933691003, -21159275264, -181405779887, -1935285600256, -10159446470927, -49976214294528, 2835996855537109, 63805712413261824 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties , arXiv:1103.2582

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 * A202273 A210702 A173177

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

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Last modified January 28 06:29 EST 2020. Contains 331317 sequences. (Running on oeis4.)