A391888 a(0)=5 and a(n) = n*(a(n-1) + 2) for n > 0.

5, 7, 18, 60, 248, 1250, 7512, 52598, 420800, 3787218, 37872200, 416594222, 4999130688, 64988698970, 909841785608, 13647626784150, 218362028546432, 3712154485289378, 66818780735208840, 1269556833968967998, 25391136679379360000, 533213870266966560042, 11730705145873264320968

Offset

0,1

References

Miklos Bona, Introduction to Enumerative and Analytic Combinatorics, CRC Press, 2025, pp. 128-130.

Links

Table of n, a(n) for n=0..22.

Formula

E.g.f.: (5 + 2*x*exp(x))/(1 - x).

a(n) = 5*n! + 2*Sum_{i=0..n-1} n!/i!.

a(n) ~ (2*e + 5)*sqrt(2*Pi)*(12*n + 1)*n^(n+1/2)*exp(-n)/(12*n).

Maple

a:= proc(n) option remember;
      `if`(n=0, 5, n*(a(n-1)+2))
    end:
seq(a(n), n=0..23);  # Alois P. Heinz, Mar 24 2026

Mathematica

a[n_]:=5n!+2Sum[n!/i!, {i, 0, n-1}]; Array[a, 23, 0]

Crossrefs

Cf. A000142, A007526, A033540, A052648, A165792.

Sequence in context: A370775 A263878 A297937 * A337349 A028319 A116640

Adjacent sequences: A391885 A391886 A391887 * A391889 A391890 A391891

Keyword

nonn,easy

Author

Stefano Spezia, Mar 24 2026

Status

approved