A048743 Triangle read by rows: T(n,k) = k!*binomial(n-1,k-1)*Stirling2(n,k), 1 <= k <= n.

1, 1, 2, 1, 12, 6, 1, 42, 108, 24, 1, 120, 900, 960, 120, 1, 310, 5400, 15600, 9000, 720, 1, 756, 27090, 168000, 252000, 90720, 5040, 1, 1778, 121716, 1428840, 4410000, 4021920, 987840, 40320, 1, 4080, 508200, 10442880, 58388400, 106686720, 65197440, 11612160, 362880

Offset

1,3

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)

Example

The 3rd row is formed from [ 1,2,6,24 ]*[ 1,3,3,1 ]*[ 1,7,6,1 ] => [ 1,42,108,24 ].
Triangle begins:
  1;
  1,2;
  1,12,6;
  1,42,108,24;
  1,120,900,960,120;

Maple

A048743 := proc(n, k) k!*binomial(n-1, k-1)*combinat[stirling2](n, k) ; end proc:
seq(seq(A048743(n, k), k=1..n), n=1..12) ; # R. J. Mathar, Aug 30 2011

Mathematica

Flatten[Table[k!Binomial[n-1, k-1]StirlingS2[n, k], {n, 10}, {k, n}]] (* Harvey P. Dale, Feb 21 2013 *)

Prog

(PARI) T(n, k)=k!*binomial(n-1, k-1)*stirling(n, k, 2) \\ Andrew Howroyd, Oct 03 2025

Crossrefs

Row sums give A045531.

Cf. A007318, A008277.

Sequence in context: A387647 A342430 A181417 * A049055 A276998 A222866

Adjacent sequences: A048740 A048741 A048742 * A048744 A048745 A048746

Keyword

easy,nonn,tabl

Author

Alford Arnold

Extensions

More terms from James Sellers, Apr 22 2000

a(43) onwards from Andrew Howroyd, Oct 03 2025

Status

approved