A191300 Expansion of exp(x*arctan(x)) = 1 + Sum_{n>0} a(n)*x^(2*n)/(2*n-1)!.

1, 1, 1, 4, -62, 3600, -312784, 39782976, -6974450160, 1614143578368, -477069128688384, 175403422124098560, -78541482962813397504, 42088662436010509209600, -26598972441544647820185600, 19578612638548987656917630976

Offset

0,4

Links

Table of n, a(n) for n=0..15.

Formula

a(n)=(2*n-1)!*sum(k=1..n, ((-1)^(n-k)*sum(i=0..2*n, (2^i*stirling1(i+k,k)*binomial(2*n-k-1,i+k-1))/(i+k)!))), n>0, a(0)=1.

Prog

(Maxima)
a(n):=(2*n-1)!*sum(((-1)^(n-k)*sum((2^i*stirling1(i+k, k)*binomial(2*n-k-1, i+k-1))/(i+k)!, i, 0, 2*n)), k, 1, n);

Crossrefs

Sequence in context: A277392 A349068 A054958 * A087613 A350282 A369725

Adjacent sequences: A191297 A191298 A191299 * A191301 A191302 A191303

Keyword

sign

Author

Vladimir Kruchinin, May 30 2011

Status

approved