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

1, 3, 20, 576, 278528, 35433480192, 299759591197780213760, 10974106333200265446693831089674524819456, 7439641733497565555964435786808198079572596514767406239535149772508418579365888

Offset

0,2

References

D. E. Knuth, Surreal Numbers, Addison-Wesley, Reading, 1974.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..11

Wikipedia, Surreal number

Formula

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

Example

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

Prog

(PARI) a(n) = sum(i=1, 2^n, i*binomial(2^n-1, i-1)); \\ Michel Marcus, Aug 08 2013

Crossrefs

Sequence in context: A365365 A189603 A203228 * A300917 A089943 A108699

Adjacent sequences: A174969 A174970 A174971 * A174973 A174974 A174975

Keyword

nonn

Author

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

Extensions

Added more terms, Michel Marcus, Aug 08 2013

Status

approved