A306226 Triangle read by rows: T(n,k) = Sum_{i=0..n/2} C(n-i,i)*C(n-i,k-i)*C(n-1,i) (0 <= k <= n).

1, 1, 1, 1, 3, 2, 1, 7, 11, 5, 1, 13, 36, 37, 13, 1, 21, 92, 160, 123, 35, 1, 31, 200, 520, 655, 401, 96, 1, 43, 387, 1405, 2575, 2541, 1293, 267, 1, 57, 686, 3325, 8295, 11711, 9492, 4131, 750, 1, 73, 1136, 7112, 23128, 43736, 50148, 34476, 13107, 2123, 1, 91, 1782, 14040, 57708, 140112, 212856, 205332, 122535, 41353, 6046

Offset

0,5

Links

Table of n, a(n) for n=0..65.

Formula

G.f.: (x*y+x+1)/(2*sqrt((-x*y-x+1)^2-4*x*y*(x*y+x)))+1/2.

Example

1;
1, 1;
1, 3, 2;
1, 7, 11, 5;
1, 13, 36, 37, 13;
1, 21, 92, 160, 123, 35;

Prog

(Maxima)
T(n, k):=sum(binomial(n-i, i)*binomial(n-i, k-i)*binomial(n-1, i), i, 0, n/2);

Crossrefs

Cf. A123160.

Cf. A005773 (right diagonal).

Sequence in context: A122832 A056151 A134436 * A186370 A163626 A028246

Adjacent sequences: A306223 A306224 A306225 * A306227 A306228 A306229

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Feb 16 2019

Status

approved