OFFSET
0,3
LINKS
Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.
FORMULA
a(n) = sum(m=1..n, sum(k=m..n, (binomial(m,k-m)*((-1)^(n-k)+1)*sum(i=0..k/2, (2*i-k)^n*binomial(k,i)*(-1)^((n+k)/2-i)))/2^k)/m!).
MATHEMATICA
With[{nn=20}, CoefficientList[Series[Exp[Sin[x]+Sin[x]^2], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 01 2017 *)
PROG
(Maxima)
a(n):=sum(sum((binomial(m, k-m)*((-1)^(n-k)+1)*sum((2*i-k)^n*binomial(k, i)*(-1)^((n+k)/2-i), i, 0, k/2))/2^k, k, m, n)/m!, m, 1, n);
CROSSREFS
KEYWORD
sign
AUTHOR
Vladimir Kruchinin, Apr 21 2011
STATUS
approved