A390798 - OEIS

A390798

a(n) = Sum_{k=0..n} (3*k+2) * binomial(5*n-2*k+2,n-k)/(5*n-2*k+2).

%I #11 Nov 23 2025 09:47:54

%S 1,3,17,124,1030,9251,87517,859099,8669363,89378119,937338385,

%T 9968284525,107246775281,1165214293500,12766501347012,140894107553484,

%U 1564845156329626,17477561474851094,196177569785319286,2211811995984100253,25037053775934416711,284438311913461647139

%N a(n) = Sum_{k=0..n} (3*k+2) * binomial(5*n-2*k+2,n-k)/(5*n-2*k+2).

%H Vincenzo Librandi, <a href="/A390798/b390798.txt">Table of n, a(n) for n = 0..920</a>

%F G.f.: g^2/(1-x*g^3) where g = 1+x*g^5 is the g.f. of A002294.

%t Table[Sum[(3*k+2)*Binomial[5*n-2*k+2,n-k]/(5*n-2*k+2),{k,0,n}],{n,0,30}] (* _Vincenzo Librandi_, Nov 23 2025 *)

%o (PARI) a(n) = sum(k=0, n, (3*k+2)*binomial(5*n-2*k+2, n-k)/(5*n-2*k+2));

%o (Magma) [&+[(3*k+2)*Binomial(5*n-2*k+2, n-k)/(5*n-2*k+2): k in [0..n]] : n in [0..30] ]; // _Vincenzo Librandi_, Nov 23 2025

%Y Cf. A118970, A390715, A390721, A390777.

%Y Cf. A002294.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 19 2025