A387873 - OEIS

%I #16 Sep 14 2025 12:54:44

%S 1,2,127,1574,25773,427351,6643782,107746282,1717012749,27481113638,

%T 439924466026,7035859329512,112595619434887,1801425114687749,

%U 28822936611339453,461170414282959151,7378682274243863442,118059247217851456567,1888946370232447241574

%N a(n) = Sum_{k=0..n} binomial(4*n+1,5*k).

%H Vincenzo Librandi, <a href="/A387873/b387873.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,130,740,-65,16).

%F G.f.: (1-3*x-13*x^2-61*x^3-22*x^4)/((1-16*x) * (1+11*x+46*x^2-4*x^3+x^4)).

%F a(n) = 5*a(n-1) + 130*a(n-2) + 740*a(n-3) - 65*a(n-4) + 16*a(n-5) for n > 4.

%t Table[Sum[Binomial[4*n+1,5*k],{k,0,n}],{n,0,20}] (* _Vincenzo Librandi_, Sep 14 2025 *)

%o (PARI) a(n) = sum(k=0, n, binomial(4*n+1, 5*k));

%o (Magma) [&+[Binomial(4*n+1, 5*k): k in [0..n]]: n in [0..20]]; // _Vincenzo Librandi_, Sep 14 2025

%Y Cf. A387848.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Sep 10 2025