A009192 E.g.f. exp(log(1+x)*cos(x)).

1, 1, 0, -3, -6, 15, 75, 84, -1820, -123, -10725, 475816, -3554562, 32763107, -501958275, 6877337128, -95130710792, 1486984480729, -24736452203529, 430314112493264, -7930867848273070, 154362838472661367, -3154456665148212743

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Programs

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 */

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

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997