A225621 -id:A225621 - cp's OEIS frontend

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

Joseph L. Pe, Oct 01 2002

			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;

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

Cf. A227550, A225621 (central terms).

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

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

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

More terms from Michel Marcus, May 19 2013

A227791 Central terms of the triangle in A227550.

Original entry on oeis.org

1, 2, 8, 36, 176, 940, 5568, 37128, 280992, 2410812, 23250080, 249164344, 2934303264, 37617633976, 521009920256, 7748175156240, 123095897716800, 2080205257723740, 37253560076385120, 704703668205036120, 14039778681732928800, 293831851498842784680

Offset: 0

Reinhard Zumkeller, Aug 05 2013

nonn

Cf. A074911, A225621, A227550.

Haskell
```
a227791 n = a227550 (2 * n) n
```

b:= proc(x, y) option remember; `if`(x=0, y!,
      b(x-1, y)+b(sort([x, y-1])[]))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..26);  # Alois P. Heinz, Jul 14 2021

T[n_, 0] := n!; T[n_, n_] := n!;
T[n_, k_] /; 0Jean-François Alcover, Nov 03 2022 *)

a(n) = A074911(2*n,n).

cp's OEIS Frontend

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

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