OFFSET
0,4
FORMULA
a(n)=sum(k=0..n, (sum(m=1..(n-k)/2, binomial(n,2*m)*(stirling1(n-2*m,k)*(sum(i=0..(k-1)/2, (k-2*i)^(2*m)*binomial(k,i)))*(-1)^(m))))/2^(k-1)+(stirling1(n,k))). - Vladimir Kruchinin, Jun 29 2011
E.g.f.: (1+x)^cos(x). - Vaclav Kotesovec, Jul 28 2018
a(n) ~ (-1)^n * n! / (Gamma(-cos(1)) * n^(1 + cos(1))). - Vaclav Kotesovec, Jul 28 2018
PROG
(Maxima)
a(n):=sum((sum(binomial(n, 2*m)*(stirling1(n-2*m, k)*(sum((k-2*i)^(2*m)*binomial(k, i), i, 0, (k-1)/2))*(-1)^(m)), m, 1, (n-k)/2))/2^(k-1)+(stirling1(n, k)), k, 0, n); /* Vladimir Kruchinin, Jun 29 2011 */
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
STATUS
approved