OFFSET
0,3
COMMENTS
The series g(x) := Sum_{n>=0} a(n) * 2^((-n*n+n)/2) * x^n / n! satisfies g'(x) = g(x/2) e^x.
The denominators of the power series can be found at A006125. - Lewis Chen, Apr 28 2019
LINKS
FiveThirtyEight, The Riddler (Apr. 26, 2019) (Riddler Express), with solution
FORMULA
a(n+1) = Sum_{n=0..k} a(k)*binomial(n, k)*2^( (n*n+n - k*k-k)/2 ).
PROG
(PARI) {a(n) = if( n<1, n==0, n--; sum(k=0, n, a(k) * binomial(n, k) * 2^( (n*n+n - k*k-k)/2 )))};
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Michael Somos, Jun 04 2018
STATUS
approved