A393911 a(n) = 1 + n*(n+1)/2 + Sum_{k=0..n-1} a(k) * a(n-1-k).

1, 3, 10, 36, 143, 618, 2836, 13565, 66839, 336779, 1726888, 8980997, 47256275, 251109662, 1345585434, 7262855090, 39450419229, 215484555365, 1182847628142, 6521704585396, 36101014071891, 200557059579272, 1117825303788580, 6248896332099798, 35028191371684041

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)^3 + x*A(x)^2.

G.f.: (1 - sqrt(1 - 4*x*(1/(1-x) + x/(1-x)^3)))/(2*x).

Mathematica

CoefficientList[Series[(1-Sqrt[1-4*x*(1/(1-x)+x/(1-x)^3)])/(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)^3)))/(2*x))
(Magma) R<x>:=PowerSeriesRing(Rationals(), 25); Coefficients(R! (1 - Sqrt(1 - 4*x*(1/(1-x) + x/(1-x)^3)))/(2*x)); // Vincenzo Librandi, Mar 07 2026

Crossrefs

Cf. A086616, A393912.

Sequence in context: A129247 A162162 A149042 * A081921 A353262 A165792

Adjacent sequences: A393908 A393909 A393910 * A393912 A393913 A393914

Keyword

nonn,easy

Author

Seiichi Manyama, Mar 02 2026

Status

approved