A378402 - OEIS

%I #10 Nov 27 2024 15:12:45

%S 1,5,49,533,6081,71365,853105,10331221,126321409,1556044805,

%T 19280812849,240054516245,3000687934401,37634567169477,

%U 473365023172209,5968699720282453,75422513665403905,954877942305602053,12109526474814388273,153801537443722913813,1956059583033416379841

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

%H Harvey P. Dale, <a href="/A378402/b378402.txt">Table of n, a(n) for n = 0..898</a>

%F a(n) = [x^n] (1 + x + (1 + x)^4)^n.

%t Table[Sum[Binomial[n,k]Binomial[n+3k,n],{k,0,n}],{n,0,20}] (* _Harvey P. Dale_, Nov 27 2024 *)

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

%Y Cf. A001850, A243116.

%Y Cf. A378378.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 25 2024