A211789 Row sums of A211788.

1, 2, 9, 50, 310, 2056, 14273, 102410, 753390, 5651948, 43074218, 332553252, 2595442616, 20443630100, 162308182577, 1297503030106, 10435055801110, 84371602316812, 685424273207630, 5592040955107420, 45798007929729828

Offset: 1

Author

Peter Bala, Aug 02 2012

Keywords

• nonn
• easy

Links

• Gheorghe Coserea, Table of n, a(n) for n = 1..303

Crossrefs

Cf. A211788.

Programs

Mathematica

Rest[CoefficientList[InverseSeries[Series[x*(2*x-1)^2/(x-1)^2, {x, 0, 30}], x], x]] (* Vaclav Kotesovec, Nov 05 2017 *)

PARI

N=21; x='x+O('x^(N+1)); Vec(serreverse(x*((1-2*x)/(1-x))^2)) \\ Gheorghe Coserea, Nov 05 2017

Formula

a(n) = Sum_{k = 1..n} A211788(n,k).

G.f. A(x) satisfies: A(x) = x*((1-A(x))/(1-2*A(x)))^2, a(n) = (Sum_{i=0..n-1} 2^i*(-1)^(n-i-1)*binomial(2*n,n-i-1)*binomial(2*n+i-1,2*n-1))/n for n > 0, a(0)=0. [Vladimir Kruchinin, Feb 08 2013]

From Vaclav Kotesovec, Nov 05 2017: (Start)

Recurrence: 4*n*(2*n - 1)*(17*n - 27)*a(n) = (1207*n^3 - 4331*n^2 + 4818*n - 1584)*a(n-1) - 2*(n-3)*(2*n - 3)*(17*n - 10)*a(n-2).

a(n) ~ sqrt(21/sqrt(17)-5) * ((71 + 17*sqrt(17))/16)^n / (sqrt(8*Pi) * n^(3/2)). (End)

a(n+1) = (1/(n+1)) * Sum_{k=0..n} binomial(2*n+k+1,k) * binomial(n-1,n-k). - Seiichi Manyama, Jan 12 2024