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 A142460 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 = 5. 9
 1, 1, 1, 1, 12, 1, 1, 83, 83, 1, 1, 514, 1826, 514, 1, 1, 3105, 28310, 28310, 3105, 1, 1, 18656, 376615, 905920, 376615, 18656, 1, 1, 111967, 4627821, 22403635, 22403635, 4627821, 111967, 1, 1, 671838, 54377008, 478781506, 940952670, 478781506 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Row sums are A047055. One of a family of triangles. For m = ...,-2,-1,0,1,2,3,4,5, ... we get ..., A225372, A144431, A007318, A008292, A060187, A142458, A142459, A142560, ... LINKS G. Strasser, Generalisation of the Euler adic, Math. Proc. Camb. Phil. Soc. 150 (2010) 241-256, Triangle A_5(n,k). FORMULA m=5; 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, 12, 1}, {1, 83, 83, 1}, {1, 514, 1826, 514, 1}, {1, 3105, 28310, 28310, 3105, 1}, {1, 18656, 376615, 905920, 376615, 18656, 1}, {1, 111967, 4627821, 22403635, 22403635, 4627821, 111967, 1}, {1, 671838, 54377008, 478781506, 940952670, 478781506, 54377008, 671838, 1}, {1, 4031069, 622333256, 9346191344, 32208325226, 32208325226, 9346191344, 622333256, 4031069, 1} MAPLE A142460 := proc(n, k) if n = k then 1; elif k > n or k < 1 then 0 ; else (5*n-5*k+1)*procname(n-1, k-1)+(5*k-4)*procname(n-1, k) ; end if; end proc: seq(seq(A142459(n, k), k=1..n), n=1..10) ; # R. J. Mathar, May 11 2013 MATHEMATICA m=5; ( 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 Cf. A225372, A144431, A007318, A008292, A060187, A142458, A142459. Sequence in context: A174672 A174151 A155491 * A156280 A166962 A022175 Adjacent sequences:  A142457 A142458 A142459 * A142461 A142462 A142463 KEYWORD nonn,tabl,easy AUTHOR Roger L. Bagula, Sep 19 2008 EXTENSIONS Edited by N. J. A. Sloane, May 08 2013, May 11 2013 STATUS approved

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Last modified April 10 01:34 EDT 2020. Contains 333392 sequences. (Running on oeis4.)