0,2

sum(n=1,inf,1/a(n))=Pi^2/18 (Euler) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 07 2002

Number of permutations of three distinct letters (ABC) 0 to n times ("-", ABC (1-1-1), AABBCC (2-2-2), AAABBBCCC (3-3-3), etc...) and one after the other to resemble motif:( ("-", AAB (2-1-0), AAAABB (4-2-0), AAAAAABBB (6-3-0), AAAAAAABBBB (8-4-0), etc... one (1) fixed point. Example:if "-" and motif "-" then 0*1 fixed point, if ABC (1-1-1) and motif AAB (2-1-0) then 2*1 fixed point, if AABBCC (2-2-2), and motif AAAABB (4-2-0) then 24*1 fixed point, if AAABBBCCC (3-3-3), and motif AAAAAABBB (6-3-0) then 180* 1 fixed point, etc. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 07 2009]

J. Ser, Les Calculs Formels des S\'{e}ries de Factorielles. Gauthier-Villars, Paris, 1933, p. 93.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

A. J. van der Poorten, A proof that Euler missed...Apery's proof of the irrationality of zeta(3), Math. Intelligencer 1 (1978/1979), 195-203.

T. D. Noe, Table of n, a(n) for n=0..200

H. J. H. Tuenter, Walking into an absolute sum

with(combinat):for n from 0 to 22 do printf(`%d, `, n*sum(binomial(2*n, n), k=1..n)) od: - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 13 2007

(Mupad) combinat::catalan(n)*(n+1)*n^2 $ n = 0..36 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 17 2007

Cf. A002736, A005258, A005259, A005429, A005430.

Sequence in context: A157053 A052411 A073066 this_sequence A131972 A059387 A126190

Adjacent sequences: A002733 A002734 A002735 this_sequence A002737 A002738 A002739

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).