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%I #31 Dec 24 2023 10:08:24
%S 2,3,6,17,66,327,1958,13701,109602,986411,9864102,108505113,
%T 1302061346,16926797487,236975164806,3554627472077,56874039553218,
%U 966858672404691,17403456103284422,330665665962404001,6613313319248080002
%N a(n) = A000522(n) + 1.
%C a(n) is an upper bound on the Ramsey numbers in A003323. - D. G. Rogers, Aug 27 2006
%C There is a nice derivation of the recurrence relation given in the Walker reference.
%H Alois P. Heinz, <a href="/A073591/b073591.txt">Table of n, a(n) for n = 0..200</a> (28 terms from Vincenzo Librandi)
%H R. C. Walker, <a href="http://www.jstor.org/stable/3615645">A graph coloring theorem</a>, Math. Gaz., 60 (1976), 54-57.
%F 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
%F a(n) = n*(a(n-1) - 1) + 2. - _Georg Fischer_, Dec 24 2023 [from the Walker reference, p. 55]
%p a:= proc(n) a(n):= `if`(n=0, 2, n*a(n-1)-n+2) end:
%p seq(a(n), n=0..30); # _Alois P. Heinz_, Feb 17 2014
%t 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)
%t Table[FunctionExpand[Gamma[n, 1] E] + 1, {n, 2, 29}] (* _Vincenzo Librandi_, Feb 17 2014 *)
%Y Cf. A000522, A001339, A003323, A007526.
%K nonn
%O 0,1
%A _Vladeta Jovovic_, Aug 28 2002
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