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 A169660 Triangle, read by rows, T(n, k) = binomial(n-1,k-1)*n!/k! + binomial(n-1, n-k)* n!/(n-k+1)! - n!. 1
 1, 1, 1, 1, 6, 1, 1, 24, 24, 1, 1, 140, 120, 140, 1, 1, 1110, 780, 780, 1110, 1, 1, 10122, 8190, 3360, 8190, 10122, 1, 1, 100856, 101976, 30240, 30240, 101976, 100856, 1, 1, 1088712, 1332576, 512064, 60480, 512064, 1332576, 1088712, 1, 1, 12700890 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Row sums are: {1, 2, 8, 50, 402, 3782, 39986, 466146, 5927186, 81594182, ...}. The first negative terms are T(11,6) = -11975040, T(12,6) = T(12,7) = -127733760, T(13,7) = -3943779840, T(14,7) = T(14,8) = -53785892160. - Hugo Pfoertner, Jul 16 2020 LINKS G. C. Greubel, Rows n = 1..100 of triangle, flattened FORMULA T(n, k) = binomial(n-1,k-1)*n!/k! + binomial(n-1, n-k)*n!/(n-k+1)! - n!. EXAMPLE Triangle begins as: 1; 1, 1; 1, 6, 1; 1, 24, 24, 1; 1, 140, 120, 140, 1; 1, 1110, 780, 780, 1110, 1; 1, 10122, 8190, 3360, 8190, 10122, 1; 1, 100856, 101976, 30240, 30240, 101976, 100856, 1; 1, 1088712, 1332576, 512064, 60480, 512064, 1332576, 1088712, 1; MAPLE b:=binomial; seq(seq( b(n-1, k-1)*n!/k! + b(n-1, n-k)*n!/(n-k+1)! -n!, k=1..n), n=1..10); # G. C. Greubel, Nov 28 2019 MATHEMATICA T[n_, k_]:= Binomial[n-1, k-1]*n!/k! +Binomial[n-1, n-k]*n!/(n-k+1)! -n!; Table[T[n, m], {n, 10}, {k, n}]//Flatten (* modified by G. C. Greubel, Nov 28 2019 *) PROG (PARI) T(n, k) = binomial(n-1, k-1)*n!/k! + binomial(n-1, n-k)*n!/(n-k+1)! - n!; \\ G. C. Greubel, Nov 28 2019 (Magma) F:=Factorial; B:=Binomial; [B(n-1, k-1)*F(n)/F(k) + B(n-1, n-k)*F(n)/F(n - k+1) - F(n): k in [1..n], n in [1..10]]; // G. C. Greubel, Nov 28 2019 (Sage) f=factorial; b=binomial; [[b(n-1, k-1)*f(n)/f(k) + b(n-1, n-k)*f(n)/f(n - k+1) - f(n) for k in (1..n)] for n in (1..10)] # G. C. Greubel, Nov 28 2019 (GAP) F:=Factorial;; B:=Binomial;; Flat(List([1..10], n-> List([1..n], k-> B(n-1, k-1)*F(n)/F(k) + B(n-1, n-k)*F(n)/F(n - k+1) - F(n) ))); # G. C. Greubel, Nov 28 2019 CROSSREFS Sequence in context: A155863 A173882 A174045 * A035348 A140945 A141688 Adjacent sequences: A169657 A169658 A169659 * A169661 A169662 A169663 KEYWORD sign,tabl AUTHOR Roger L. Bagula, Apr 05 2010 STATUS approved

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Last modified August 2 22:39 EDT 2024. Contains 374875 sequences. (Running on oeis4.)