A071740 Expansion of (1+x^3*C^4)*C^3, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.

1, 3, 9, 29, 97, 332, 1155, 4069, 14482, 51986, 187986, 684114, 2503573, 9207590, 34013895, 126153045, 469574670, 1753616370, 6568462590, 24670834470, 92896573770, 350612243904, 1326145316766, 5026028589314, 19083966487332, 72588567045652, 276550811157796

Offset

0,2

Links

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

Formula

a(n) = binomial(2*n+1, n+1) - binomial(2*n, n-2) - binomial(2*n, n-4) for n > 3. - Mélika Tebni, Apr 20 2026

Maple

a := n -> binomial(2*n+1, n+1) - binomial(2*n, n-2) - binomial(2*n, n-4):
seq(a(n), n = 0 .. 26); # Mélika Tebni, Apr 20 2026

Mathematica

With[{c=(1-Sqrt[1-4x])/(2x)}, CoefficientList[Series[(1+x^3 c^4)c^3, {x, 0, 30}], x]] (* Harvey P. Dale, Nov 18 2018 *)

Prog

(PARI) my(x='x+O(x^50), C = (1-(1-4*x)^(1/2))/(2*x)); Vec((1+x^3*C^4)*C^3) \\ Michel Marcus, Apr 20 2026

Crossrefs

Cf. A000108.

Sequence in context: A148938 A082306 A124431 * A081696 A247172 A339843

Adjacent sequences: A071737 A071738 A071739 * A071741 A071742 A071743

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 06 2002

Status

approved