A199482 a(n) is defined by exp(x^2*cotan(x)) = Sum_(n>=0) a(n)*x^n/n!^2.

1, 1, 2, -6, -168, -2600, -10800, 727440, 43263360, 1032103296, -228614400, -3068098387200, -194799891686400, -9157262446126080, 406734380101969920, 68528048007234816000, 9942165414475886592000, 179947145139068340633600, -678953675518129505894400

Offset

0,3

Links

Table of n, a(n) for n=0..18.

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)!)))))/m!), a(0)=1.

Example

exp(x^2*cot(x)) = 1+x+(1/2)*x^2-(1/6)*x^3-(7/24)*x^4-(13/72)*x^5-(1/48)*x^6+(433/15120)*x^7+(1073/40320)*x^8+(14221/1814400)*x^9-(1/57600)*x^10-...

Maple

t1 := exp(x^2*cot(x));
t2 := series(t1, x, 21);
t3 := seriestolist(t2);
t4 := [seq(t3[n]*(n-1)!^2, n=1..nops(t3))]; # N. J. A. Sloane, Aug 25 2019

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!, m, 1, n);

Crossrefs

Sequence in context: A323841 A281819 A329980 * A168649 A135937 A182523

Adjacent sequences: A199479 A199480 A199481 * A199483 A199484 A199485

Keyword

sign

Author

Vladimir Kruchinin, Nov 06 2011

Status

approved