A173621 Triangle of Generalized Runyon numbers R_{n,k}^(4) read by rows.

1, 1, 4, 1, 12, 22, 1, 24, 120, 140, 1, 40, 380, 1140, 969, 1, 60, 920, 5060, 10626, 7084, 1, 84, 1890, 16380, 61425, 98280, 53820, 1, 112, 3472, 43400, 251720, 704816, 906192, 420732, 1, 144, 5880, 99960, 824670, 3518592, 7791168, 8347680, 3362260

Offset

1,3

Comments

The Runyon numbers R_{n,k}^(1) are A001263, R_{n,k}^(2) are A108767. Row sums are in A002294.

References

Chunwei Song, The Generalized Schroeder Theory, El. J. Combin. 12 (2005) #R53

Links

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

Formula

T(n,k) = R(n,k,4) with R(n,k,m)= binomial(n,k)*binomial(m*n,k-1)/n, 1<=k<=n.

T(n,n) = A002293(n).

T(n,n-1) = A004332(n).

T(n,2) = A046092(n-1).

Example

The triangle starts in row n=1 as
1;
1, 4;
1, 12, 22;
1, 24, 120, 140;
1, 40, 380, 1140, 969;
1, 60, 920, 5060, 10626, 7084;
1, 84, 1890, 16380, 61425, 98280, 53820;
1, 112, 3472, 43400, 251720, 704816, 906192, 420732;

Crossrefs

Sequence in context: A117413 A322970 A157384 * A274087 A105197 A157398

Adjacent sequences: A173618 A173619 A173620 * A173622 A173623 A173624

Keyword

easy,nonn,tabl

Author

R. J. Mathar, Nov 08 2010

Status

approved