A166979 Triangle T(n,k) read by rows: T(n, k) = (m*n - m*k + 1)*T(n - 1, k - 1) + (9*k - 8)*(m*k - (m - 1))*T(n - 1, k) where m = 0.

1, 1, 1, 1, 11, 1, 1, 111, 30, 1, 1, 1111, 681, 58, 1, 1, 11111, 14050, 2305, 95, 1, 1, 111111, 278061, 78590, 5820, 141, 1, 1, 1111111, 5394270, 2478581, 293930, 12306, 196, 1, 1, 11111111, 103602241, 74794538, 13353991, 860006, 23086, 260, 1, 1

Offset

1,5

Comments

Row sums are: {1, 2, 13, 143, 1852, 27563, 473725, 9290396, 203745235, 4912490375,...}.

Links

G. C. Greubel, Table of n, a(n) for n = 1..325

Formula

T(n, k) = T(n - 1, k - 1) + (9*k - 8)*T(n - 1, k).

Example

{1},
{1, 1},
{1, 11, 1},
{1, 111, 30, 1},
{1, 1111, 681, 58, 1},
{1, 11111, 14050, 2305, 95, 1},
{1, 111111, 278061, 78590, 5820, 141, 1},
{1, 1111111, 5394270, 2478581, 293930, 12306, 196, 1},
{1, 11111111, 103602241, 74794538, 13353991, 860006, 23086, 260, 1},
{1, 111111111, 1979553690, 2197849305, 568892205, 52914267, 2129736, 39726, 333, 1}

Mathematica

A[n_, 1] := 1; A[n_, n_] := 1; A[n_, k_] := (m*n - m*k + 1)A[n - 1, k - 1] + (9*k - 8)*(m*k - (m - 1))A[n - 1, k]; Table[A[n, k] /. m -> 0, {n, 10}, {k, n}] // Flatten  (* This sequence is the case of m=0 *)

Crossrefs

Cf. A002275.

Sequence in context: A014469 A157149 A342889 * A022174 A173006 A015125

Adjacent sequences: A166976 A166977 A166978 * A166980 A166981 A166982

Keyword

nonn,tabl

Author

Roger L. Bagula, Oct 26 2009

Status

approved