OFFSET
0,4
LINKS
Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.
FORMULA
E.g.f.: exp(sin(x)-sin(x)^2).
a(n) = Sum_(m=1..n, Sum_(k=m..n, (-1)^(k-m)*(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!), n>0, a(0)=1.
MATHEMATICA
With[{nn=20}, CoefficientList[Series[Exp[Sin[x]-Sin[x]^2], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jan 27 2015 *)
PROG
(Maxima)
a(n):=sum(sum((-1)^(k-m)*(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