OFFSET
1,4
COMMENTS
Sum_{k >= 1} b(k) = e^(3/2) where e = 2.718... . More generally if b(1) = b(2) = ... = b(m) = 1 and b(n+m+1) = 1/(n+m)*( b(n+m) + b(n+m-1) + ... + b(n) ) then Sum_{k >= 1} b(k) = e^H(m) where H(m) = Sum_{j=1..m} 1/j is the m-th harmonic number (Benoit Cloitre and Boris Gourevitch).
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..350
FORMULA
a(n) = denominator( A013989(n-1)/n! ). - G. C. Greubel, Aug 17 2022
MATHEMATICA
Table[Denominator[n*(-I/Sqrt[2])^(n-1)*HermiteH[n-1, I/Sqrt[2]]/n!], {n, 30}] (* G. C. Greubel, Aug 17 2022 *)
PROG
(Magma)
A013989:= func< n | (&+[Factorial(n)/(2^k*Factorial(n-2*k)*Factorial(k)): k in [0..Floor(n/2)]]) >;
[A069944(n): n in [1..30]]; // G. C. Greubel, Aug 17 2022
(SageMath)
@CachedFunction
[denominator(A013989(n-1)/factorial(n)) for n in (1..30)] # G. C. Greubel, Aug 17 2022
CROSSREFS
KEYWORD
easy,frac,nonn
AUTHOR
Benoit Cloitre, Apr 27 2002
STATUS
approved