A391994 - OEIS

%I #12 Jan 10 2026 19:16:14

%S 0,0,-1,0,2,8,17,32,52,80,115,160,214,280,357,448,552,672,807,960,

%T 1130,1320,1529,1760,2012,2288,2587,2912,3262,3640,4045,4480,4944,

%U 5440,5967,6528,7122,7752,8417,9120,9860,10640,11459,12320,13222,14168,15157,16192,17272

%N Expansion of (x^2*(3*x - 1))/((x - 1)^4*(x + 1)).

%H Paolo Xausa, <a href="/A391994/b391994.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).

%F a(n) = (n^3 - 3*n^2 - n + 3*(n mod 2)) / 6.

%F A392248row(k) = n -> a(n)*n + A002620(n)*n^2.

%p a := n -> (n^3 - 3*n^2 - n + 3*irem(n, 2))/6: seq(a(n), n = 0..48);

%t A391994[n_] := (3*Mod[n, 2] + n*((n - 3)*n - 1))/6; Array[A391994, 50, 0] (* or *)

%t LinearRecurrence[{3, -2, -2, 3, -1}, {0, 0, -1, 0, 2}, 50] (* _Paolo Xausa_, Jan 10 2026 *)

%Y Cf. A392248, A002620.

%K sign,easy

%O 0,5

%A _Peter Luschny_, Jan 09 2026