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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 06 2004
EXTENSIONS
Changed offset to 1. - Michael Somos, Nov 30 2016
STATUS
approved