A393231 Expansion of x^2 * (3+x-x^2) / (1-x)^4.

0, 3, 13, 33, 66, 115, 183, 273, 388, 531, 705, 913, 1158, 1443, 1771, 2145, 2568, 3043, 3573, 4161, 4810, 5523, 6303, 7153, 8076, 9075, 10153, 11313, 12558, 13891, 15315, 16833, 18448, 20163, 21981, 23905, 25938, 28083, 30343, 32721, 35220, 37843, 40593, 43473, 46486, 49635, 52923

Offset

1,2

Comments

Row sums (excluding the last two terms) of the triangular view of A001477 (the nonnegative integers).

Links

Table of n, a(n) for n=1..47.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = (n-1) * (n^2+2*n-2) / 2.

E.g.f.: (1/2) * exp(x) * (x^3 + 4*x^2 - 2*x + 2) - 1.

Mathematica

a[n_] := (n-1)*(n^2 + 2*n - 2)/2; Array[a, 50] (* Amiram Eldar, Feb 07 2026 *)

Crossrefs

Cf. A001477.

Sequence in context: A032586 A147137 A146230 * A166805 A252979 A332366

Adjacent sequences: A393228 A393229 A393230 * A393232 A393233 A393234

Keyword

nonn,easy

Author

Enrique Navarrete, Feb 06 2026

Status

approved