A132007 Triangle, read by rows, where T(n,k) = T(n,k-1) + n*T(n-1,k-1) for n>0 and k>0, with T(n,0) = T(n-1,n-1) for n>0 and T(0,0) = 1.

1, 1, 2, 2, 4, 8, 8, 14, 26, 50, 50, 82, 138, 242, 442, 442, 692, 1102, 1792, 3002, 5212, 5212, 7864, 12016, 18628, 29380, 47392, 78664, 78664, 115148, 170196, 254308, 384704, 590364, 922108, 1472756, 1472756, 2102068, 3023252, 4384820, 6419284

Offset

0,3

Comments

Column 0 and main diagonal (offset) equals A110083.

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Formula

T(n+1,0) = Sum_{k=0..n} (n!/k!)*C(n,k)*T(k,0) for n>=0 with T(0,0)=1.

Example

Triangle begins:
1;
1, 2;
2, 4, 8;
8, 14, 26, 50;
50, 82, 138, 242, 442;
442, 692, 1102, 1792, 3002, 5212;
5212, 7864, 12016, 18628, 29380, 47392, 78664;
78664, 115148, 170196, 254308, 384704, 590364, 922108, 1472756;
1472756, 2102068, 3023252, 4384820, 6419284, 9496916, 14219828, 21596692, 33378740; ...

Mathematica

T[n_, k_] := T[n, k] = If[k < 0 || n < k, 0, If[n == 0 && k == 0, 1, If[k == 0, T[n - 1, n - 1], T[n, k - 1] + n*T[n - 1, k - 1]]]]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, Dec 15 2017 *)

Prog

(PARI) T(n, k)=if(k<0 || n<k, 0, if(n==0 && k==0, 1, if(k==0, T(n-1, n-1), T(n, k-1)+n*T(n-1, k-1))))

Crossrefs

Cf. A110083 (column 0); A132008 (row sums).

Sequence in context: A283241 A101651 A325880 * A094605 A217662 A085619

Adjacent sequences: A132004 A132005 A132006 * A132008 A132009 A132010

Keyword

nonn,tabl

Author

Paul D. Hanna, Aug 07 2007

Status

approved