A212422 Sums involving triangle A096815.

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

Links

Table of n, a(n) for n=0..29.

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

Cf. A096815, A096816, A212264, A212265, A212421.

Sequence in context: A034769 A219017 A285216 * A189832 A193062 A193061

Adjacent sequences: A212419 A212420 A212421 * A212423 A212424 A212425

Keyword

nonn

Author

Emanuele Munarini, May 16 2012

Status

approved