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A142461 Triangle read by rows: T(n,k) (1<=k<=n) given by T(n, 1) = T(n,n) = 1, otherwise T(n, k) = (m*n-m*k+1)*T(n-1,k-1)+(m*k-m+1)*T(n-1,k), where m = 6. 6
1, 1, 1, 1, 14, 1, 1, 111, 111, 1, 1, 796, 2886, 796, 1, 1, 5597, 52642, 52642, 5597, 1, 1, 39210, 824271, 2000396, 824271, 39210, 1, 1, 274507, 11931033, 58614299, 58614299, 11931033, 274507, 1, 1, 1921592, 165260188, 1483533704, 2930714950 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are A047657.

LINKS

Table of n, a(n) for n=1..41.

G. Strasser, Generalisation of the Euler adic, Math. Proc. Camb. Phil. Soc. 150 (2010) 241-256, Triangle A_6(n,k).

FORMULA

m=6; t(n,k,m)=(m*n - m*k + 1)t(n - 1, k - 1) + (m*k - (m-1))t(n - 1, k).

EXAMPLE

{1},

{1, 1},

{1, 14, 1},

{1, 111, 111, 1},

{1, 796, 2886, 796, 1},

{1, 5597, 52642, 52642, 5597, 1},

{1, 39210, 824271, 2000396, 824271, 39210, 1},

{1, 274507, 11931033, 58614299, 58614299, 11931033, 274507, 1},

{1, 1921592, 165260188, 1483533704, 2930714950, 1483533704, 165260188, 1921592, 1},

{1, 13451193, 2231010900, 34301767332, 119257418574, 119257418574, 34301767332, 2231010900, 13451193, 1}

MATHEMATICA

m=6; ( Pascal level: k=N-1) A[n_, 1] := 1; A[n_, n_] := 1; A[n_, k_] := (m*n - m*k + 1)A[n - 1, k - 1] + (m*k - (m - 1))A[n - 1, k]; a = Table[A[n, k], {n, 10}, {k, n}]; Flatten[a]

CROSSREFS

For m = ...,-2,-1,0,1,2,3,4,5,6,7, ... we get ..., A225372, A144431, A007318, A008292, A060187, A142458, A142459, A142460, ...

Sequence in context: A157278 A144441 A157150 * A174720 A060628 A022177

Adjacent sequences:  A142458 A142459 A142460 * A142462 A142463 A142464

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula, Sep 19 2008

EXTENSIONS

Edited by N. J. A. Sloane, May 08 2013

STATUS

approved

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Last modified April 1 04:58 EDT 2020. Contains 333155 sequences. (Running on oeis4.)