A073591 a(n) = A000522(n) + 1.

2, 3, 6, 17, 66, 327, 1958, 13701, 109602, 986411, 9864102, 108505113, 1302061346, 16926797487, 236975164806, 3554627472077, 56874039553218, 966858672404691, 17403456103284422, 330665665962404001, 6613313319248080002

Offset: 0

Author

Vladeta Jovovic, Aug 28 2002

Keywords

• nonn

Comments

a(n) is an upper bound on the Ramsey numbers in A003323. - D. G. Rogers, Aug 27 2006

There is a nice derivation of the recurrence relation given in the Walker reference.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200 (28 terms from Vincenzo Librandi)
• R. C. Walker, A graph coloring theorem, Math. Gaz., 60 (1976), 54-57.

Crossrefs

Cf. A000522, A001339, A003323, A007526.

Programs

Maple

a:= proc(n) a(n):= `if`(n=0, 2, n*a(n-1)-n+2) end:
seq(a(n), n=0..30);  # Alois P. Heinz, Feb 17 2014

Mathematica

f[n_] := n*(f[n - 1] - 1) + 2;f[0]=2; ff[n_]:=(1/(1+n))(1+E*Gamma[1+n, 1]-E*(n^2)*Gamma[1+n, 1]+E*n*Gamma[2+n, 1]) (Spindler)
Table[FunctionExpand[Gamma[n, 1] E] + 1, {n, 2, 29}] (* Vincenzo Librandi, Feb 17 2014 *)

Formula

Conjecture: a(n) +(-n-2)*a(n-1) +(2*n-1)*a(n-2) +(-n+2)*a(n-3)=0. - R. J. Mathar, Feb 16 2014

a(n) = n*(a(n-1) - 1) + 2. - Georg Fischer, Dec 24 2023 [from the Walker reference, p. 55]