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 A278333 a(n) = A278332(n+1)/(n+1) for n>=0. 1

%I

%S 1,1,3,22,181,2111,31471,563305,11634169,275850685

%N a(n) = A278332(n+1)/(n+1) for n>=0.

%C E.g.f. of A278332 equals the limit of the average of all permutations of the compositions of the functions x*exp(x^k), for k=1..n, as n increases.

%e E.g.f.: A(x) = 1 + x + 3*x^2/2! + 22*x^3/3! + 181*x^4/4! + 2111*x^5/5! + 31471*x^6/6! + 563305*x^7/7! + 11634169*x^8/8! + 275850685*x^9/9! +...

%e RELATED SERIES.

%e log(A(x)) = x + 2*x^2/2! + 15*x^3/3! + 96*x^4/4! + 1100*x^5/5! + 15870*x^6/6! + 278817*x^7/7! + 5558616*x^8/8! + 129258684*x^9/9! +...

%Y Cf. A278332.

%K nonn,more

%O 0,3

%A _Paul D. Hanna_, Nov 18 2016

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Last modified February 28 01:54 EST 2020. Contains 332319 sequences. (Running on oeis4.)