A087413 a(n) = Sum_{k=1..n} C(3*k,k)/3.
1, 6, 34, 199, 1200, 7388, 46148, 291305, 1853580, 11868585, 76380825, 493606725, 3201081873, 20821158233, 135776966761, 887393271310, 5811082966885, 38119865826420, 250447855600320, 1647729357535485, 10854207824989830, 71581930485576630
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..200
Programs
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Mathematica
Table[Sum[Binomial[3*k,k]/3,{k,1,n}],{n,1,20}] (* Vaclav Kotesovec, Oct 14 2012 *) -
PARI
a(n)=sum(k=1,n,binomial(3*k,k))/3 \\ Charles R Greathouse IV, Nov 10 2011
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PARI
a=vector(99,i,1);for(n=2,#a,a[n]=a[n-1]+binomial(3*n,n)/3);a \\ Charles R Greathouse IV, Nov 10 2011
Formula
G.f.: 1/((3*g-1)*(g^3-2*g^2+g-1)*(g-1)^2) where g*(1-g)^2 = x. - Mark van Hoeij, Nov 10 2011
Recurrence: 2*n*(2*n-1)*a(n) = (31*n^2-29*n+6)*a(n-1) - 3*(3*n-2)*(3*n-1)*a(n-2). - Vaclav Kotesovec, Oct 14 2012
a(n) ~ 3^(3*n+5/2)/(23*2^(2*n+1)*sqrt(Pi)*sqrt(n)). - Vaclav Kotesovec, Oct 14 2012
a(n) = Sum_{k=1..n} binomial(3*k-1,k-1). [Bruno Berselli, Oct 10 2015]