A393912 a(n) = 1 + binomial(n+2,3) + Sum_{k=0..n-1} a(k) * a(n-1-k).

1, 3, 11, 42, 171, 751, 3509, 17135, 86331, 445161, 2337097, 12448148, 67095277, 365264609, 2005444499, 11091616038, 61738014131, 345581890401, 1944078165249, 10985238037766, 62322123340849, 354849796233957, 2027085961125183, 11614483110130587, 66729581614802773

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

G.f. A(x) satisfies A(x) = 1/(1-x) + x/(1-x)^4 + x*A(x)^2.

G.f.: (1 - sqrt(1 - 4*x*(1/(1-x) + x/(1-x)^4)))/(2*x).

Mathematica

CoefficientList[Series[(1-Sqrt[1-4*x*(1/(1-x)+x/(1-x)^4)])/(2*x), {x, 0, 25}], x] (* Vincenzo Librandi, Mar 07 2026 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec((1-sqrt(1-4*x*(1/(1-x)+x/(1-x)^4)))/(2*x))
(Magma) R<x>:=PowerSeriesRing(Rationals(), 25); Coefficients(R! (1 - Sqrt(1 - 4*x*(1/(1-x) + x/(1-x)^4)))/(2*x)); // Vincenzo Librandi, Mar 07 2026

Crossrefs

Cf. A086616, A393911.

Sequence in context: A200030 A084782 A149068 * A151088 A149069 A151089

Adjacent sequences: A393909 A393910 A393911 * A393913 A393914 A393915

Keyword

nonn,easy

Author

Seiichi Manyama, Mar 02 2026

Status

approved