A111805 Number triangle T(n,k)=binomial(2(n+k),4k).

1, 1, 1, 1, 15, 1, 1, 70, 45, 1, 1, 210, 495, 91, 1, 1, 495, 3003, 1820, 153, 1, 1, 1001, 12870, 18564, 4845, 231, 1, 1, 1820, 43758, 125970, 74613, 10626, 325, 1, 1, 3060, 125970, 646646, 735471, 230230, 20475, 435, 1, 1, 4845, 319770, 2704156, 5311735

Offset

0,5

Comments

Related to matchings of the complete graph K_2n: T(n,k)=A100861(2(n+k),2k)/f(2k), where f(n)=(2n-1)!! Column k gives number of standard tableaux of shape (2n+1,1^(4k)).

Links

Table of n, a(n) for n=0..49.

Formula

Column k has g.f. x^k*sum{j=0..2k+1, binomial(4k+1, 2j)x^j}/(1-x)^(4k+1)

Example

Rows begin
1;
1,1;
1,15,1;
1,70,45,1;
1,210,495,91,1;

Mathematica

Table[Binomial[2(n+k), 4k], {n, 0, 10}, {k, 0, n}]//Flatten (* Harvey P. Dale, Mar 30 2019 *)

Crossrefs

Sequence in context: A070644 A174389 A176286 * A238754 A176226 A155493

Adjacent sequences: A111802 A111803 A111804 * A111806 A111807 A111808

Keyword

easy,nonn,tabl

Author

Paul Barry, Aug 17 2005

Status

approved