A121398 Main diagonal of triangle A121400; also equals the partial sums of column 0 (A121399) of the same triangle.

1, 2, 5, 11, 28, 70, 184, 486, 1313, 3576, 9851, 27319, 76286, 214120, 603858, 1709719, 4857959, 13845948, 39572583, 113380652, 325576692, 936796592, 2700456452, 7797587816, 22550434989, 65308288346, 189388557677

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Formula

G.f. A(x) = A(x^2*G)*G*(1-x^2*G)/(1-x), where G(x) is the g.f. of the Motzkin numbers (A001006): G = (1 + x*G + x^2*G^2).

Prog

(PARI) {a(n)=local(F=1+x+x^2, G=serreverse(x/(F+x^2*O(x^n)))/x, H=1+x, A); for(i=0, n, H=G*subst(H, x, x^2*G)+x^2*O(x^n)); A=(x*H-y*subst(H, x, x*y))/(x*subst(F, x, y)-y); polcoeff(polcoeff(A, n, x), n, y)}

Crossrefs

Cf. A121400 (triangle), A121399 (column 0), A001006 (Motzkin).

Sequence in context: A174145 A358451 A124016 * A359181 A000625 A202476

Adjacent sequences: A121395 A121396 A121397 * A121399 A121400 A121401

Keyword

nonn

Author

Paul D. Hanna, Jul 27 2006

Status

approved