A387204 a(n) = n*(n + 1)*(n^2 + 17*n + 54)/24.

0, 6, 23, 57, 115, 205, 336, 518, 762, 1080, 1485, 1991, 2613, 3367, 4270, 5340, 6596, 8058, 9747, 11685, 13895, 16401, 19228, 22402, 25950, 29900, 34281, 39123, 44457, 50315, 56730, 63736, 71368, 79662, 88655, 98385, 108891, 120213, 132392, 145470, 159490, 174496

Offset: 0

Author

Peter Luschny, Aug 27 2025

Keywords

• nonn
• easy
• new

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A387152 (row 4).

Programs

Maple

a := n -> n*(n + 1)*(n^2 + 17*n + 54)/24: seq(a(n), n = 0..41);

Mathematica

A387204[n_] := n*(n + 1)*(n*(n + 17) + 54)/24;
Array[A387204, 50, 0] (* Paolo Xausa, Aug 29 2025 *)

Formula

a(n) = [x^n] (-2*x^3 + 7*x^2 - 6*x)/(x - 1)^5.

a(n) = [x^n] Pochhammer(x, 4)*(x + 1)^n.