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
KEYWORD
AUTHOR
Wouter Meeussen, Jun 06 2001
STATUS
approved