A262394 - OEIS

%I #18 Nov 10 2022 07:42:51

%S 1,4,20,110,637,3808,23256,144210,904475,5722860,36463440,233646504,

%T 1504152860,9721421440,63040282096,409972529754,2672860120455,

%U 17464206951100,114330456032100,749760805916430

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

%H G. C. Greubel, <a href="/A262394/b262394.txt">Table of n, a(n) for n = 1..1000</a>

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

%F a(n) = (n+2) * binomial(3*n, n-1) / (3*n). - _Vaclav Kotesovec_, Sep 21 2015

%t Table[Sum[k Binomial[n, k-1] Binomial[2n, n-k], {k, n}]/n, {n, 30}] (* _Michael De Vlieger_, Sep 21 2015 *)

%o (Maxima)

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

%o (PARI) a(n)=sum(k=1,n,(k*binomial(n,k-1)*binomial(2*n,n-k))/n) \\ _Anders Hellström_, Sep 21 2015

%o (Magma) [(n+2)*Binomial(3*n,n)/(3*(2*n+1)): n in [1..30]]; // _G. C. Greubel_, Nov 09 2022

%o (SageMath) [(n+2)*binomial(3*n,n)/(3*(2*n+1)) for n in range(1,31)] # _G. C. Greubel_, Nov 09 2022

%Y Cf. A001764.

%K nonn

%O 1,2

%A _Vladimir Kruchinin_, Sep 21 2015