A255139 a(n) = n! - Fibonacci(n).

1, 0, 1, 4, 21, 115, 712, 5027, 40299, 362846, 3628745, 39916711, 479001456, 6227020567, 87178290823, 1307674367390, 20922789887013, 355687428094403, 6402373705725416, 121645100408827819, 2432902008176633235, 51090942171709429054

Offset

0,4

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = A000142(n) - A000045(n).

E.g.f.: 1/(1 - x) - 2*exp(x/2)*sinh(sqrt(5)*x/2)/sqrt(5). - Ilya Gutkovskiy, Dec 27 2016

Example

For n = 0, a(0) = 0! - F(0) = 1 - 0 = 1.

Maple

A255139 := proc(n)
    n!-combinat[fibonacci](n) ;
end proc: # R. J. Mathar, Jul 08 2015

Mathematica

Table[n! - Fibonacci[n], {n, 0, 20}]

Prog

(PARI) vector(30, n, n--; n! - fibonacci(n)) \\ Michel Marcus, Jul 05 2015

Crossrefs

Cf. A000142, A000045, A080568 (the sum instead of the difference).

Sequence in context: A190089 A349300 A240436 * A015554 A024051 A180908

Adjacent sequences: A255136 A255137 A255138 * A255140 A255141 A255142

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Jul 03 2015

Status

approved