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

1,2

Links

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A211788.

Sequence in context: A115599 A047069 A225006 * A192945 A271960 A175895

Adjacent sequences: A211786 A211787 A211788 * A211790 A211791 A211792

Keyword

nonn,easy

Author

Peter Bala, Aug 02 2012

Status

approved