A262394 a(n) = (1/n)*Sum_{k=1..n} k*binomial(n,k-1)*binomial(2*n,n-k).

1, 4, 20, 110, 637, 3808, 23256, 144210, 904475, 5722860, 36463440, 233646504, 1504152860, 9721421440, 63040282096, 409972529754, 2672860120455, 17464206951100, 114330456032100, 749760805916430

Offset: 1

Author

Vladimir Kruchinin, Sep 21 2015

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001764.

Programs

Magma

[(n+2)*Binomial(3*n,n)/(3*(2*n+1)): n in [1..30]]; // G. C. Greubel, Nov 09 2022

Mathematica

Table[Sum[k Binomial[n, k-1] Binomial[2n, n-k], {k, n}]/n, {n, 30}] (* Michael De Vlieger, Sep 21 2015 *)

Maxima

a(n):=sum(k*binomial(n,k-1)*binomial(2*n,n-k),k,1,n)/n;

PARI

a(n)=sum(k=1,n,(k*binomial(n,k-1)*binomial(2*n,n-k))/n) \\ Anders Hellström, Sep 21 2015

SageMath

[(n+2)*binomial(3*n,n)/(3*(2*n+1)) for n in range(1,31)] # G. C. Greubel, Nov 09 2022

Formula

G.f.: x*B'(x) + B(x) - B'(x)/B(x) - 1, where B(x) is g.f. of A001764.

a(n) = (n+2) * binomial(3*n, n-1) / (3*n). - Vaclav Kotesovec, Sep 21 2015