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A173621
Triangle of Generalized Runyon numbers R_{n,k}^(4) read by rows.
0
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
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
KEYWORD
easy,nonn,tabl
AUTHOR
R. J. Mathar, Nov 08 2010
STATUS
approved