cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

Original entry on oeis.org

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

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Author

Paul D. Hanna, Aug 07 2007

Keywords

Comments

Column 0 and main diagonal (offset) equals A110083.

Examples

			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; ...
		

Crossrefs

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

Programs

  • 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 *)
  • PARI
    T(n,k)=if(k<0 || n
    				

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.