A387251 - OEIS

%I #33 Jan 03 2026 05:20:01

%S 0,3,144,2187,20736,151875,944784,5250987,26873856,129140163,

%T 590490000,2593609227,11019960576,45535459203,183742537104,

%U 726413416875,2821109907456,10785915553923,40669853253264,151467076640907,557885504160000,2034339951272643,7351201499765904,26345121306126507

%N a(n) = 3^n*n^4.

%H Paolo Xausa, <a href="/A387251/b387251.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (15,-90,270,-405,243).

%F a(n) = 15*a(n-1) - 90*a(n-2) + 270*a(n-3) - 405*a(n-4) + 243*a(n-5).

%F G.f.: 3*x*(1 + 3*x)*(1 + 30*x + 9*x^2)/(1 - 3*x)^5.

%F E.g.f.: (27*x^3 + 54*x^2 + 21*x + 1)*(3*x)*exp(3*x).

%t A387251[n_] := 3^n*n^4; Array[A387251, 25, 0] (* _Paolo Xausa_, Jan 02 2026 *)

%o (PARI) a(n) = 3^n * n^4; \\ _Michael B. Porter_, Dec 22 2025

%Y Cf. A000244, A000583, A036290, A062074, A127960.

%K nonn,easy

%O 0,2

%A _Enrique Navarrete_, Dec 16 2025