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A155493 A recursive triangle transformed in a Narayana numbers way: m=4;a(n,k)=(m*n - m*k + 1)*a(n - 1, k - 1) + (m*k - (m - 1))*a(n - 1, k); t(n,m)=((n+1)!/(m+1)!*(n-m+1)!)*a(n,m). 0
1, 1, 1, 1, 15, 1, 1, 118, 118, 1, 1, 770, 3540, 770, 1, 1, 4671, 67810, 67810, 4671, 1, 1, 27321, 1039689, 3085355, 1039689, 27321, 1, 1, 156220, 14006244, 99524810, 99524810, 14006244, 156220, 1, 1, 878868, 173788752, 2602528824, 6090918372 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 17, 238, 5082, 144964, 5219377, 227374550, 11645311262, 686243339548,...}.

LINKS

Table of n, a(n) for n=0..40.

FORMULA

m=4;a(n,k)=(m*n - m*k + 1)*a(n - 1, k - 1) + (m*k - (m - 1))*a(n - 1, k);

t(n,m)=((n+1)!/(m+1)!*(n-m+1)!)*a(n,m).

EXAMPLE

{1},

{1, 1},

{1, 15, 1},

{1, 118, 118, 1},

{1, 770, 3540, 770, 1},

{1, 4671, 67810, 67810, 4671, 1},

{1, 27321, 1039689, 3085355, 1039689, 27321, 1},

{1, 156220, 14006244, 99524810, 99524810, 14006244, 156220, 1},

{1, 878868, 173788752, 2602528824, 6090918372, 2602528824, 173788752, 878868, 1},

{1, 4882765, 2040080700, 59194475160, 281882231148, 281882231148, 59194475160, 2040080700, 4882765, 1}

MATHEMATICA

Clear[A, a0, b0, n, k, m];

(* general m-th recursion *)

A[n_, 1, m_] := 1; A[n_, n_, m_] := 1;

A[n_, k_, m_] := (m*n - m*k + 1)*A[n - 1, k - 1, m] + (m*k - (m - 1))*A[n - 1, k, m];

f[n_] = Product[k + 1, {k, 0, n}]; a0[n_, m_] = f[n]/(f[m]*f[n - m]);

m = 4; Table[a0[n - 1, k - 1]*A[n, k, m], {n, 10}, {k, n}];

Flatten[%]

CROSSREFS

Sequence in context: A111805 A238754 A176226 * A156939 A174187 A174693

Adjacent sequences:  A155490 A155491 A155492 * A155494 A155495 A155496

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Jan 23 2009

STATUS

approved

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Last modified October 14 09:25 EDT 2019. Contains 327995 sequences. (Running on oeis4.)