A120278 Sum[Sum[C(2k,k),{k,1,m}],{m,1,n}], where C(2k,k)=(2k)!/(k!)^2=A000984[k].

2, 10, 38, 136, 486, 1760, 6466, 24042, 90238, 341190, 1297574, 4958114, 19019254, 73196994, 282492254, 1092867904, 4236849774, 16455966944, 64020347914, 249431257704, 973100041934, 3800867789884, 14862066265434, 58170868424084

Offset

1,1

Comments

a(2(p-1)) is divisible by p^2 for p=7,13,19,31,37,43,61,67.. A002476 Primes of form 6n + 1.

Links

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

Formula

a(n) = Sum[Sum[(2k)!/(k!)^2,{k,1,m}],{m,1,n}].

a(n) = 2 * Sum[ A079309[k], {k,1,n} ] = Sum[ A066796[k], {k,1,n} ]. - Alexander Adamchuk, Sep 01 2006

G.f.: x*(1/Sqrt[1-4*x]-1)/(x(x-1)^2) [From Harvey P. Dale, May 24 2011]

Recurrence: n*a(n) = 2*(3*n-1)*a(n-1) - (9*n-4)*a(n-2) + 2*(2*n-1)*a(n-3). - Vaclav Kotesovec, Oct 19 2012

a(n) ~ 2^(2*n+4)/(9*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 19 2012

Mathematica

Table[Sum[Sum[(2k)!/(k!)^2, {k, 1, m}], {m, 1, n}], {n, 1, 50}]
CoefficientList[Series[(1/Sqrt[1-4 x]-1)/((x-1)^2 x), {x, 0, 50}], x] (* Harvey P. Dale, May 24 2011 *)

Crossrefs

Cf. A000984, A066796, A002476.

Cf. A066796, A079309.

Sequence in context: A281199 A081956 A056182 * A166898 A143960 A122117

Adjacent sequences: A120275 A120276 A120277 * A120279 A120280 A120281

Keyword

nonn

Author

Alexander Adamchuk, Jul 04 2006

Status

approved