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A260786 Twice the Euler or up/down numbers A000111. 4


%S 2,2,2,4,10,32,122,544,2770,15872,101042,707584,5405530,44736512,

%T 398721962,3807514624,38783024290,419730685952,4809759350882,

%U 58177770225664,740742376475050,9902996106248192,138697748786275802,2030847773013704704,31029068327114173810,493842960380415967232

%N Twice the Euler or up/down numbers A000111.

%H S. T. Thompson, <a href="/A260786/a260786.pdf">Problem E754: Skew Ordered Sequences</a>, Amer. Math. Monthly, 54 (1947), 416-417. [Annotated scanned copy]

%F a(0)=a(1)=2; thereafter a(n) = (1/4)*Sum_{k=1..n} binomial(n-1, k-1)*a(k-1)*a(n-k).

%p f:=proc(n) option remember;

%p if n <= 1 then 2 else (1/4)*add(binomial(n-1,k-1)*f(k-1)*f(n-k),k=1..n); fi;

%p end;

%p [seq(f(n),n=0..30)];

%Y Cf. A000111.

%Y Apart from initial terms, same as A001250.

%K nonn

%O 0,1

%A _N. J. A. Sloane_, Aug 04 2015

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Last modified September 24 10:48 EDT 2021. Contains 347642 sequences. (Running on oeis4.)