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
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; ...
Links
- G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
Programs
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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 *)
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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.
Comments