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A073591 A000522(n)+1. 4
2, 3, 6, 17, 66, 327, 1958, 13701, 109602, 986411, 9864102, 108505113, 1302061346, 16926797487, 236975164806, 3554627472077, 56874039553218, 966858672404691, 17403456103284422, 330665665962404001, 6613313319248080002 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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

Vincenzo Librandi and 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.

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

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 *)

CROSSREFS

Cf. A003323, A001339.

Sequence in context: A024498 A319283 A325298 * A114491 A122939 A321399

Adjacent sequences:  A073588 A073589 A073590 * A073592 A073593 A073594

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Aug 28 2002

STATUS

approved

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Last modified January 17 04:29 EST 2021. Contains 340214 sequences. (Running on oeis4.)