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A212422
Sums involving triangle A096815.
2
1, 2, 4, 11, 30, 79, 212, 574, 1588, 4455, 12478, 35377, 100335, 285385, 812648, 2318781, 6620447, 18935754, 54209820, 155482355, 446673973, 1284474758, 3698559438, 10659129412, 30740979089, 88719378807, 256240088606, 740502848865, 2141552451104, 6197576727082
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