A391994 Expansion of (x^2*(3*x - 1))/((x - 1)^4*(x + 1)).

0, 0, -1, 0, 2, 8, 17, 32, 52, 80, 115, 160, 214, 280, 357, 448, 552, 672, 807, 960, 1130, 1320, 1529, 1760, 2012, 2288, 2587, 2912, 3262, 3640, 4045, 4480, 4944, 5440, 5967, 6528, 7122, 7752, 8417, 9120, 9860, 10640, 11459, 12320, 13222, 14168, 15157, 16192, 17272

Offset

0,5

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

Formula

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

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

Maple

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

Mathematica

A391994[n_] := (3*Mod[n, 2] + n*((n - 3)*n - 1))/6; Array[A391994, 50, 0] (* or *)
LinearRecurrence[{3, -2, -2, 3, -1}, {0, 0, -1, 0, 2}, 50] (* Paolo Xausa, Jan 10 2026 *)

Crossrefs

Cf. A392248, A002620.

Sequence in context: A066564 A357576 A034972 * A294537 A294548 A061150

Adjacent sequences: A391991 A391992 A391993 * A391995 A391996 A391997

Keyword

sign,easy

Author

Peter Luschny, Jan 09 2026

Status

approved