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

Author

R. H. Hardin

Keywords

• sign
• easy

Links

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

Programs

Mathematica

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

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 */

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

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

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