A257532 Triangle, read by rows, T(n,k)=k/n*Sum_{i=0..n-k} C(2*n,n-k-i)*C(2*n+i-1,i).

1, 4, 1, 24, 8, 1, 172, 64, 12, 1, 1360, 536, 120, 16, 1, 11444, 4672, 1156, 192, 20, 1, 100520, 42024, 11088, 2096, 280, 24, 1, 911068, 387456, 106908, 22016, 3420, 384, 28, 1, 8457504, 3643448, 1038984, 227408, 39120, 5192, 504, 32, 1

Offset

1,2

Links

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

Formula

G.f.: 1/(1-x*B(x)^2*y)-1, where B(x) is g.f. of A027307.

G.f. satisfies A(x)=x*[(1+A(x))/(1-A(x))]^2.

Example

1;
4, 1;
24, 8, 1;
172, 64, 12, 1;
1360, 536, 120, 16, 1;

Prog

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

Crossrefs

Cf. A027307. First column = A032349.

Sequence in context: A166027 A158978 A128417 * A183875 A136232 A079621

Adjacent sequences: A257529 A257530 A257531 * A257533 A257534 A257535

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Apr 28 2015

Status

approved