A074911 Triangle generated by Pascal's rule, except begin and end the n-th row with n!.

1, 2, 2, 6, 4, 6, 24, 10, 10, 24, 120, 34, 20, 34, 120, 720, 154, 54, 54, 154, 720, 5040, 874, 208, 108, 208, 874, 5040, 40320, 5914, 1082, 316, 316, 1082, 5914, 40320, 362880, 46234, 6996, 1398, 632, 1398, 6996, 46234, 362880

Offset: 1

Author

Joseph L. Pe, Oct 01 2002

Keywords

• easy
• nonn
• tabl

Examples

			Triangle begins:
1;
2, 2;
6, 4, 6;
24, 10, 10, 24;
120, 34, 20, 34, 120;
720, 154, 54, 54, 154, 720;
5040, 874, 208, 108, 208, 874, 5040;
		

Links

• Reinhard Zumkeller, Rows n = 1..100 of table, flattened

Crossrefs

Cf. A227550, A225621 (central terms).

Programs

Haskell

a074911 n k = a074911_tabl !! (n-1) !! (k-1)
a074911_row n = a074911_tabl !! (n-1)
a074911_tabl = map fst $ iterate
   (\(vs, w:ws) -> (zipWith (+) ([w] ++ vs) (vs ++ [w]), ws))
   ([1], tail a001563_list)
-- Reinhard Zumkeller, Aug 05 2013

Mathematica

T[n_, 1] := n!;
T[n_, n_] := n!;
T[n_, k_] /; 1Jean-François Alcover, Nov 03 2022 *)

PARI

t(n, k) = {if (k<1 || k>n, return (0)); if (k==1 || k==n, return (n!)); return (t(n-1, k-1) + t(n-1, k));}
tabl(nn) = {for (n=1, nn, for (k=1, n, print1(t(n, k), ", ");); print(););} \\ Michel Marcus, May 19 2013

Extensions

More terms from Michel Marcus, May 19 2013