A199540 Expansion 1/(1-x^2*cotan(x)) = Sum_{n>=0} a(n)*x^n/(n)!^2.

1, 1, 4, 24, 192, -320, -138240, -10214400, -669204480, -43782488064, -2628064051200, -91419903590400, 14288196206592000, 5367226212019077120, 1259862249808204922880, 257126813359346810880000, 46529454048255997378560000

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = n!^2*sum(m=1..n, (2^(n-2*m)*(-1)^((n-m)/2)*sum(l=0..m, (2^l*l! *C(m,l)* sum(k=0..n-2*m+l, (k!*stirling1(l+k,l)*stirling2(n-2*m+l,k))/ ((l+k)!*(n-2*m+l)!)))))), a(0)=1.

Prog

(Maxima) a(n):=if n=0 then 1 else n!^2*sum((2^(n-2*m)*(-1)^((n-m)/2) *sum((2^l*l! *binomial(m, l)* sum((k!*stirling1(l+k, l)*stirling2(n-2 *m+l, k))/((l+k)!*(n-2*m+l)!), k, 0, n-2*m+l)), l, 0, m)), m, 1, n);

Crossrefs

Sequence in context: A366367 A367144 A193854 * A259868 A036691 A349514

Adjacent sequences: A199537 A199538 A199539 * A199541 A199542 A199543

Keyword

sign

Author

Vladimir Kruchinin, Nov 07 2011

Status

approved