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

1,2

Links

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

Example

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;

Mathematica

T[n_, 1] := n!;
T[n_, n_] := n!;
T[n_, k_] /; 1<k<n := T[n, k] = T[n-1, k]+T[n-1, k-1];
Table[T[n, k], {n, 1, 9}, {k, 1, n}] // Flatten (* Jean-François Alcover, Nov 03 2022 *)

Prog

(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
(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

Crossrefs

Cf. A227550, A225621 (central terms).

Sequence in context: A249796 A182411 A067804 * A174222 A071059 A256468

Adjacent sequences: A074908 A074909 A074910 * A074912 A074913 A074914

Keyword

easy,nonn,tabl

Author

Joseph L. Pe, Oct 01 2002

Extensions

More terms from Michel Marcus, May 19 2013

Status

approved