0,4

Column 0 forms A102223.

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.

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],...

(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]))}

Cf. A008459, A102220, A102223.

Sequence in context: A099447 A078067 A009126 this_sequence A084301 A058022 A139344

Adjacent sequences: A102219 A102220 A102221 this_sequence A102223 A102224 A102225

nonn,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), Dec 31 2004