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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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified May 22 15:13 EDT 2019. Contains 323480 sequences. (Running on oeis4.)