A191471 E.g.f. (1+arctan(x))^arctan(x)

1, 0, 2, -3, 4, -30, 162, -252, 400, -27912, 200744, 705672, -4202296, -223340208, 1418238416, 29398266888, -114981277184, -8193860510784, 30889433635776, 2261786651427072, -3830504174333824

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

Mathematica

With[{nn=30}, CoefficientList[Series[(1+ArcTan[x])^ArcTan[x], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Nov 01 2011 *)

Prog

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

Crossrefs

Sequence in context: A326829 A064858 A007114 * A354729 A305205 A356905

Adjacent sequences: A191468 A191469 A191470 * A191472 A191473 A191474

Keyword

sign

Author

Vladimir Kruchinin, Jun 03 2011

Status

approved