A381787 G.f. A(x) satisfies A(x) = (1 + x) * C(x*A(x)), where C(x) is the g.f. of A000108.

1, 2, 5, 22, 112, 623, 3664, 22405, 141002, 907228, 5940663, 39459873, 265228359, 1800608563, 12328843910, 85040632504, 590371016188, 4121775003434, 28921911896836, 203854515625194, 1442669458817907, 10247020573880520, 73024240955785936, 521973882076798493

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = Sum_{k=0..n} binomial(3*k+1,k) * binomial(k+1,n-k)/(3*k+1).

Prog

(PARI) a(n) = sum(k=0, n, binomial(3*k+1, k)*binomial(k+1, n-k)/(3*k+1));

Crossrefs

Cf. A167422, A381785, A381786.

Cf. A000108.

Sequence in context: A278439 A126797 A101206 * A294467 A177251 A041807

Adjacent sequences: A381784 A381785 A381786 * A381788 A381789 A381790

Keyword

nonn

Author

Seiichi Manyama, Mar 07 2025

Status

approved