OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
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
MATHEMATICA
Table[Sum[k Binomial[n, k-1] Binomial[2n, n-k], {k, n}]/n, {n, 30}] (* Michael De Vlieger, Sep 21 2015 *)
PROG
(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
(Magma) [(n+2)*Binomial(3*n, n)/(3*(2*n+1)): n in [1..30]]; // G. C. Greubel, Nov 09 2022
(SageMath) [(n+2)*binomial(3*n, n)/(3*(2*n+1)) for n in range(1, 31)] # G. C. Greubel, Nov 09 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Sep 21 2015
STATUS
approved