A199541 Expansion x^2*cotan(x)/(exp(x^2*cotan(x))-1) = Sum_{n>=0} a(n)*x^n/(n+1)!^2.

1, -2, 3, 96, -820, 5760, 189000, 1720320, 1632960, 1393459200, 430921814400, 2452488192000, 204726089018880, 8224795200061440, 10001273371689600000, 47991858533498880000, -33369402947130515865600

Offset

0,2

Links

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

Formula

a(n) = (n+1)!^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)!)))*bernoulli(m)/(m)!), n>0, a(0)=1.

Prog

(Maxima) a(n):=if n=0 then 1 else (n+1)!^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)*bern(m)/(m)!, m, 1, n);

Crossrefs

Sequence in context: A291932 A247652 A132499 * A208205 A128931 A323463

Adjacent sequences: A199538 A199539 A199540 * A199542 A199543 A199544

Keyword

sign

Author

Vladimir Kruchinin, Nov 07 2011

Status

approved