A369491 a(n) = n! * [x^n] (2*x - 4*exp(x) + 3*exp(2*x) + 3) / 2.

1, 2, 4, 10, 22, 46, 94, 190, 382, 766, 1534, 3070, 6142, 12286, 24574, 49150, 98302, 196606, 393214, 786430, 1572862, 3145726, 6291454, 12582910, 25165822, 50331646, 100663294, 201326590, 402653182, 805306366, 1610612734, 3221225470, 6442450942, 12884901886, 25769803774

Offset: 0

Author

Peter Luschny, Jan 24 2024

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A033484 (similar, 'missing' 2).

Programs

Maple

gf := ((x + 1)*(2*x^2 - 2*x + 1))/((2*x - 1)*(x - 1)):
ser := series(gf, x, 40): seq(coeff(ser, x, n), n = 0..34);
a := proc(n) option remember; ifelse(n < 4, [1, 2, 4, 10][n+1],
3*a(n - 1) - 2*a(n - 2)) end: seq(a(n), n = 0..34);

Mathematica

LinearRecurrence[{3, -2}, {1, 2, 4, 10}, 50] (* Paolo Xausa, Feb 27 2024 *)

Formula

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

a(n) = 3*a(n - 1) - 2*a(n - 2) for n >= 4.