login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A211789 Row sums of A211788. 3
1, 2, 9, 50, 310, 2056, 14273, 102410, 753390, 5651948, 43074218, 332553252, 2595442616, 20443630100, 162308182577, 1297503030106, 10435055801110, 84371602316812, 685424273207630, 5592040955107420, 45798007929729828 (list; graph; refs; listen; history; text; internal format)
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)

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 15 19:43 EDT 2021. Contains 342977 sequences. (Running on oeis4.)