A199568 Triangle T(n,m) = coefficient of x^n (x^2*cosech(x))^m=sum(n>=m, T(n,m)x^n*m!^2/n!^2)

1, 0, 1, -6, 0, 1, 0, -48, 0, 1, 280, 0, -200, 0, 1, 0, 8640, 0, -600, 0, 1, -52080, 0, 99960, 0, -1470, 0, 1, 0, -4300800, 0, 689920, 0, -3136, 0, 1, 27651456, 0, -110557440, 0, 3429216, 0, -6048, 0, 1

Offset

1,4

Comments

Triangle T(n,m)*m!^2/n!^2=

1. Riordan Array (1,x^2*cosech(x)) without first column.

2. Riordan Array (x*cosech(x),x^2*cosech(x)) numbering triangle (0,0).

Links

Table of n, a(n) for n=1..45.

Formula

T(n,m) = n!^2/m!*sum(i=0..n-m, (2^i*m^(n-m-i)*sum(k=0..i, (stirling2(i,k)*k!*stirling1(m+k,m))/(m+k)!))/(i!*(n-m-i)!)).

Example

T(n,m)*m!^2/n!^2=
1,
0, 1,
-1/6, 0, 1,
0, -1/3, 0, 1,
7/360, 0, -1/2, 0, 1,
0,1/15, 0,-2/3, 0, 1,
-31/15120, 0, 17/120, 0, -5/6, 0, 1

Prog

(Maxima)
T(n, m):=n!^2/m!*sum((2^i*m^(n-m-i)*sum((stirling2(i, k)*k!*stirling1(m+k, m))/(m+k)!, k, 0, i))/(i!*(n-m-i)!), i, 0, n-m);

Crossrefs

Sequence in context: A264808 A200229 A137785 * A134899 A076413 A154305

Adjacent sequences: A199565 A199566 A199567 * A199569 A199570 A199571

Keyword

sign,tabl

Author

Vladimir Kruchinin, Nov 08 2011

Status

approved