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

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

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]

Mathematica

Table[Sum[Binomial[3*k, k]/3, {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Oct 14 2012 *)

Prog

(PARI) a(n)=sum(k=1, n, binomial(3*k, k))/3 \\ Charles R Greathouse IV, Nov 10 2011
(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

Crossrefs

Cf. A188675: Sum_{k=0..n} binomial(3*k,k).

Cf. A263134: Sum_{k=0..n} binomial(3*k+1,k).

Sequence in context: A126501 A370224 A218990 * A337906 A244829 A059228

Adjacent sequences: A087410 A087411 A087412 * A087414 A087415 A087416

Keyword

nonn,easy

Author

Benoit Cloitre, Oct 21 2003

Status

approved