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 A144431 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 = -1. 9
 1, 1, 1, 1, 0, 1, 1, -1, -1, 1, 1, -2, 2, -2, 1, 1, -3, 2, 2, -3, 1, 1, -4, 7, -8, 7, -4, 1, 1, -5, 9, -5, -5, 9, -5, 1, 1, -6, 16, -26, 30, -26, 16, -6, 1, 1, -7, 20, -28, 14, 14, -28, 20, -7, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,12 COMMENTS Row sums are: {1, 2, 2, 0, 0, 0, 0, 0, 0, 0, ...}. For m = ...,-1,0,1,2 we get ..., A144431, A007318 (Pascal), A008292, A060187, ..., so this might be called a sub-Pascal triangle. The triangle starts off like A098593, but is different further on. LINKS FORMULA m=-1; A(n,k) := (m*n - m*k + 1)*A(n-1, k-1) + (m*k - (m-1))*A(n-1, k). EXAMPLE Triangle begins:   1;   1,   1;   1,   0,   1;   1,  -1,  -1,   1;   1,  -2,   2,  -2,   1;   1,  -3,   2,   2,  -3,   1;   1,  -4,   7,  -8,   7,  -4,   1;   1,  -5,   9,  -5,  -5,   9,  -5,   1;   1,  -6,  16, -26,  30, -26,  16,  -6,   1;   1,  -7,  20, -28,  14,  14, -28,  20,  -7,   1;   ... MAPLE T:=proc(n, k, l) option remember; if (n=1 or k=1 or k=n) then 1 else (l*n-l*k+1)*T(n-1, k-1, l)+(l*k-l+1)*T(n-1, k, l); fi; end; for n from 1 to 8 do lprint([seq(T(n, k, -1), k=1..n)]); od; # N. J. A. Sloane, May 08 2013 MATHEMATICA m=-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. A007318, A008292, A060187, A098593. Sequence in context: A104754 A206827 A098593 * A053821 A076545 A162246 Adjacent sequences:  A144428 A144429 A144430 * A144432 A144433 A144434 KEYWORD tabl,sign AUTHOR Roger L. Bagula, Oct 04 2008 EXTENSIONS Edited by N. J. A. Sloane, May 08 2013 STATUS approved

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Last modified April 7 19:49 EDT 2020. Contains 333306 sequences. (Running on oeis4.)