The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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: A239020 A293211 A330778 * A019130 A245348 A174551 Adjacent sequences:  A061309 A061310 A061311 * A061313 A061314 A061315 KEYWORD nonn,tabl,easy AUTHOR Wouter Meeussen, Jun 06 2001 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 17 19:36 EDT 2021. Contains 343988 sequences. (Running on oeis4.)