A096745 Column with index 1 of triangle A096744, which shifts one place diagonally left and upward under the matrix cube operation.

1, 1, 3, 6, 16, 40, 133, 429, 1696, 6583, 29167, 128401, 615653, 2958117, 15028861, 76857851, 407990489, 2184026420, 11995664112, 66461796492, 375029195862, 2133759026832, 12304892986311, 71492951054537, 419663091288141

Offset

1,3

Links

Table of n, a(n) for n=1..25.

Formula

T(n,0) = 1, T(n,n) = 1, T(n,1) = Sum_{i=0,..,n-1}( Sum_{j=0,..,n-2}( T(n-2,j)*T( j,i)*T(i,0) )). - G. C. Greubel, Nov 30 2016

Mathematica

T[n_, 0] := 1; T[n_, n_] := 1; T[n_, k_] := Sum[ T[n - 2, j]*T[j, i]*T[i, k-1], {j, 0, n - 2}], {i, 0, j}] ; Table[T[n, 1], {n, 1, 10}] (* G. C. Greubel, Nov 29 2016 *)
a[n_, k_: 1] := a[n, k] = Which[n < 0 || n < k, 0, k == 0 || k == n, 1, True, Sum[a[n - 2, j] a[j, i] a[i, k - 1], {j, 0, n - 2}, {i, 0, j}]]; (* Michael Somos, Nov 30 2016 *)

Crossrefs

Cf. A096744, A096746.

Sequence in context: A018022 A166536 A128720 * A293949 A027088 A027102

Adjacent sequences: A096742 A096743 A096744 * A096746 A096747 A096748

Keyword

nonn

Author

Paul D. Hanna, Jul 06 2004

Extensions

Changed offset to 1. - Michael Somos, Nov 30 2016

Status

approved