A153592 Triangle read by rows: T(n,k) = T(n-1,k-1) +T(n-1,k) +n*(n-1)*T(n-2,k-1) for n>4 and 1<=k<=n.

2, 3, 3, 2, 20, 2, 2, 58, 58, 2, 2, 100, 516, 100, 2, 2, 162, 2356, 2356, 162, 2, 2, 248, 6718, 26384, 6718, 248, 2, 2, 362, 16038, 165038, 165038, 16038, 362, 2, 2, 508, 34256, 664772, 2229724, 664772, 34256, 508, 2, 2, 690, 67344, 2142448, 17747916

Offset

1,1

Links

Table of n, a(n) for n=1..50.

Formula

T(1,1)=2. T(2,k)=3. T(3,1) = T(3,3) =T(4,1)= T(4,4)= 2. T(3,2)=20. T(4,2)=T(4,3)=58. Otherwise T(n,k) = T(n-1,k-1) +T(n-1,k) + n*(n-1)*T(n-2,k-1).

Example

2;
3,3;
2,20,2;
2,58,58,2;
2,100,516,100,2;
2,162,2356,2356,162,2;
2,248,6718,26384,6718,248,2;
2,362,16038,165038,165038,16038,362,2;
2,508,34256,664772,2229724,664772,34256,508,2;
2,690,67344,2142448,17747916,17747916,2142448,67344,690,2;

Mathematica

Clear[A]; A[2, 1] := A[2, 2] = 3; A[3, 2] = 20;
A[4, 2] = 58; A[4, 3] = 58;
A[n_, 1] := 2; A[n_, n_] := 2;
A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + n*(n - 1)*A[n - 2, k - 1];
a = Table[A[n, k], {n, 10}, {k, n}];
Flatten[a] Table[Apply[Plus, a[[n]]], {n, 1, 10}]; Table[Apply[Plus, a[[n]]]/(n + 1)!, {n, 1, 10}];

Crossrefs

Cf. A000142 (row sums).

Sequence in context: A153310 A155688 A215490 * A351188 A153878 A118925

Adjacent sequences: A153589 A153590 A153591 * A153593 A153594 A153595

Keyword

nonn,tabl

Author

Roger L. Bagula and Gary W. Adamson, Dec 29 2008

Status

approved