A199916 Triangle T(n,k) = coefficient of x^n in expansion of ((2-2*cos(x))/x)^k = sum(n>=k, T(n,k) * x^n * (2*k)!/(n+k)!).

1, 0, 1, -1, 0, 1, 0, -5, 0, 1, 1, 0, -14, 0, 1, 0, 21, 0, -30, 0, 1, -1, 0, 147, 0, -55, 0, 1, 0, -85, 0, 627, 0, -91, 0, 1, 1, 0, -1408, 0, 2002, 0, -140, 0, 1, 0, 341, 0, -11440, 0, 5278, 0, -204, 0, 1, -1, 0, 13013, 0, -61490, 0, 12138, 0, -285, 0, 1, 0

Offset

1,8

Comments

Triangle T(n,k)*(2*k)!/(n+k)!)=

1. Riordan Array (1,(2-2*cos(x))/x) without first column.

2. Riordan Array ((2-2*cos(x))/x^2,(2-2*cos(x))/x) numbering triangle (0,0).

Links

Table of n, a(n) for n=1..67.

Formula

T(n,k):=((-1)^k*2^k*((-1)^(n+k)+1)*sum(j=1..k, ((sum(i=0..(j-1)/2, (j-2*i)^(n+k)*binomial(j,i))) *binomial(k,j)*(-1)^((n+k)/2+k-j))/2^j))/(2*k)!

Example

1
0, 1
-1, 0, 1
0, -5, 0, 1
1, 0, -14, 0, 1
0, 21, 0, -30, 0, 1
-1, 0, 147, 0, -55, 0, 1

Prog

(Maxima)
T(n, k):=((-1)^k*2^k*((-1)^(n+k)+1)*sum(((sum((j-2*i)^(n+k)*binomial(j, i), i, 0, (j-1)/2))*binomial(k, j)*(-1)^((n+k)/2+k-j))/2^j, j, 1, k))/(2*k)!

Crossrefs

Sequence in context: A277031 A085198 A339207 * A363041 A180494 A200653

Adjacent sequences: A199913 A199914 A199915 * A199917 A199918 A199919

Keyword

sign,tabl

Author

Vladimir Kruchinin, Nov 11 2011

Status

approved