OFFSET
0,2
FORMULA
S(n,k) = sum(k=0..n, T(n,k) * T(n+1,k+1) ), where T(n,k) = A096815(n,k).
MATHEMATICA
T[n_, k_] := T[n, k] = If[n < k || k < 0, 0, If[k = 1 || k == n, 1, Sum[T[n-k, j]T[k, k-j], {j, 0, k}]]]
Table[Sum[T[n, k]T[n+1, k+1], {k, 0, n}], {n, 0, 50}]
PROG
(Maxima) T(n, k):= if ( n<k or k<0 ) then 0 else
if ( k<=1 or k=n ) then 1 else sum(T(n-k, j)*T(k, k-j), j, 0, k);
makelist(sum(T(n, k)*T(n+1, k+1), k, 0, n), n, 0, 14);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emanuele Munarini, May 16 2012
STATUS
approved