A102222 Logarithm of triangular matrix A102220, which equals [2*I - A008459]^(-1).

0, 1, 0, 3, 4, 0, 22, 27, 9, 0, 323, 352, 108, 16, 0, 7906, 8075, 2200, 300, 25, 0, 290262, 284616, 72675, 8800, 675, 36, 0, 14919430, 14222838, 3486546, 395675, 26950, 1323, 49, 0, 1022475715, 954843520, 227565408, 24793216, 1582700, 68992, 2352, 64, 0

Offset

0,4

Comments

Column 0 forms A102223.

Links

Table of n, a(n) for n=0..44.

Formula

T(n, k) = C(n, k)^2*A102223(n-k). T(n, 0) = A102223(n). T(n, n) = 0 for n>=0. [A102222] = Sum_{m=1..inf} [A008459 - I]^m/m.

Example

Rows begin:
[0],
[1,0],
[3,4,0],
[22,27,9,0],
[323,352,108,16,0],
[7906,8075,2200,300,25,0],
[290262,284616,72675,8800,675,36,0],...
which equals the term-by-term product of column 0
with the squared binomial coefficients (A008459):
[(0)1^2],
[(1)1^2,(0)1^2],
[(3)1^2,(1)2^2,(0)1^2],
[(22)1^2,(3)3^2,(1)3^2,(0)1^2],
[(323)1^2,(22)4^2,(3)6^2,(1)4^2,(0)1^2],...

Prog

(PARI) {T(n, k)=if(n<k|k<0, 0, sum(m=1, n, (matrix(n+1, n+1, i, j, binomial(i-1, j-1)^2-if(i==j, 1, 0))^m/m)[n+1, k+1]))}

Crossrefs

Cf. A008459, A102220, A102223.

Sequence in context: A192442 A009126 A322278 * A171657 A287696 A366465

Adjacent sequences: A102219 A102220 A102221 * A102223 A102224 A102225

Keyword

nonn,tabl

Author

Paul D. Hanna, Dec 31 2004

Status

approved