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A096745
Column with index 1 of triangle A096744, which shifts one place diagonally left and upward under the matrix cube operation.
2
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
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
Sequence in context: A018022 A166536 A128720 * A293949 A027088 A027102
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 06 2004
EXTENSIONS
Changed offset to 1. - Michael Somos, Nov 30 2016
STATUS
approved