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 A061312 Triangle T[n,m]: T[n,-1] = 0; T[0,0] = 0; T[n,0] = n*n!; T[n,m] = T[n,m-1] - T[n-1,m-1]. 5
 0, 1, 1, 4, 3, 2, 18, 14, 11, 9, 96, 78, 64, 53, 44, 600, 504, 426, 362, 309, 265, 4320, 3720, 3216, 2790, 2428, 2119, 1854, 35280, 30960, 27240, 24024, 21234, 18806, 16687, 14833, 322560, 287280, 256320, 229080, 205056, 183822, 165016, 148329 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Appears in the (n,k)-matching problem A076731. [Johannes W. Meijer, Jul 27 2011] LINKS G. C. Greubel, Rows n=0..100 of triangle, flattened FORMULA T[n,m] = T[n,m-1]-T[n-1,m-1] with T[n,-1] = 0 and T[n,0] = A001563(n) = n*n! T(n,m) = sum(((-1)^j)*binomial(m+1,j)*(n+1-j)!, j=0..m+1) [Johannes W. Meijer, Jul 27 2011] EXAMPLE 0, 1, 1, 4, 3, 2, 18, 14, 11, 9, 96, 78, 64, 53, 44, 600, 504, 426, 362, 309, 265, 4320, 3720, 3216, 2790, 2428, 2119, 1854, 35280, 30960, 27240, 24024, 21234, 18806, 16687, 14833, MAPLE A061312 := proc(n, m): add(((-1)^j)*binomial(m+1, j)*(n+1-j)!, j=0..m+1) end: seq(seq(A061312(n, m), m=0..n), n=0..7); # Johannes W. Meijer, Jul 27 2011 MATHEMATICA T[n_, k_]:= Sum[(-1)^j*Binomial[k + 1, j]*(n + 1 - j)!, {j, 0, k + 1}]; Table[T[n, k], {n, 0, 100}, {k, 0, n}] // Flatten  (* G. C. Greubel, Aug 13 2018 *) PROG (PARI) for(n=0, 20, for(k=0, n, print1(sum(j=0, k+1, (-1)^j*binomial(k+1, j) *(n-j+1)!), ", "))) \\ G. C. Greubel, Aug 13 2018 (MAGMA) [[(&+[(-1)^j*Binomial(k+1, j)*Factorial(n-j+1): j in [0..k+1]]): k in [0..n]]: n in [0..20]]; // G. C. Greubel, Aug 13 2018 CROSSREFS Cf. A061018. From Johannes W. Meijer, Jul 27 2011: (Start) Columns: A001563, A001564, A001565, A001688, A001689, A023044, A023045, A023046, A023047; A000166, A000255, A055790; The row sums equal A193465. (End) Sequence in context: A319541 A239020 A293211 * A019130 A245348 A174551 Adjacent sequences:  A061309 A061310 A061311 * A061313 A061314 A061315 KEYWORD nonn,tabl,easy AUTHOR Wouter Meeussen, Jun 06 2001 STATUS approved

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Last modified December 11 07:47 EST 2019. Contains 329914 sequences. (Running on oeis4.)