A180623 Expansion of exp(x^2*cosec(x)).

1, 1, 1, 4, 30, 320, 5400, 119040, 3432240, 125927424, 5594520960, 302070988800, 19179742982400, 1423835230371840, 121909715166919680, 11901225092146790400, 1316846634449778432000, 163453208505912970444800

Offset

1,4

Links

Table of n, a(n) for n=1..18.

Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

Formula

B(x):=exp(x^2*cosec(x))=sum(n>=0, b(n)*x^n) b(n)=sum((if n=m then 1 else if oddp(n-m) then 0 else sum((-1)^k*(sum(binomial(k,j)*1/2^(j-1)*sum((-1)^((n-m)/2-i)*binomial(j,i)*(j-2*i)^(n-m+j)/(n-m+j)!,i,0,floor(j/2))*(-1)^(k-j),j,1,k))*binomial(k+m-1,m-1),k,1,n-m))/m!,m,1,n), a(n)=(n-1)!*n!*b(n), n>0;

Prog

(Maxima) a(n):=n!*(n-1)!*sum((if n=m then 1 else if oddp(n-m) then 0 else sum((-1)^k*(sum(binomial(k, j)*1/2^(j-1)*sum((-1)^((n-m)/2-i)*binomial(j, i)*(j-2*i)^(n-m+j)/(n-m+j)!, i, 0, floor(j/2))*(-1)^(k-j), j, 1, k))*binomial(k+m-1, m-1), k, 1, n-m))/m!, m, 1, n);

Crossrefs

Sequence in context: A298244 A293191 A367963 * A128329 A211828 A277759

Adjacent sequences: A180620 A180621 A180622 * A180624 A180625 A180626

Keyword

nonn

Author

Vladimir Kruchinin, Sep 13 2010

Status

approved