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 A174972 Number of surreal number forms produced by the n-th iteration of the induction rule. 1

%I

%S 1,3,20,576,278528,35433480192,299759591197780213760,

%T 10974106333200265446693831089674524819456,

%U 7439641733497565555964435786808198079572596514767406239535149772508418579365888

%N Number of surreal number forms produced by the n-th iteration of the induction rule.

%H Alois P. Heinz, <a href="/A174972/b174972.txt">Table of n, a(n) for n = 0..11</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Surreal_number">Surreal number</a>

%F a(n) = Sum_{i=1..2^n} i*C(2^n-1,i-1).

%e a(0) = 1*C(0,0)=1.

%e a(1) = 1*C(1,0)+2*C(1,1)=3.

%e a(2) = 1*C(3,0)+2*C(3,1)+3*C(3,2)+4*C(3,3)=20.

%o (PARI) a(n) = sum(i=1, 2^n, i*binomial(2^n-1, i-1)); \\ _Michel Marcus_, Aug 08 2013

%K nonn

%O 0,2

%A Ryan M. Smail (SmailRM2304(AT)gmail.com), Apr 02 2010

%E Added more terms, _Michel Marcus_, Aug 08 2013

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Last modified January 22 09:39 EST 2022. Contains 350481 sequences. (Running on oeis4.)