1,4

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).

G. C. Greubel, Table of n, a(n) for n = 1..350

A069943(n)/a(n) = A000085(n-1)/A000142(n-1) in lowest terms. - Christian G. Bower, Jan 14 2006

a(n) = denominator( A013989(n-1)/n! ). - G. C. Greubel, Aug 17 2022

Table[Denominator[n*(-I/Sqrt[2])^(n-1)*HermiteH[n-1, I/Sqrt[2]]/n!], {n, 30}] (* G. C. Greubel, Aug 17 2022 *)

(Magma)

A013989:= func< n | (&+[Factorial(n)/(2^k*Factorial(n-2*k)*Factorial(k)): k in [0..Floor(n/2)]]) >;

A069944:= func< n | Denominator(A013989(n-1)/Factorial(n-1)) >;

[A069944(n): n in [1..30]]; // G. C. Greubel, Aug 17 2022

(SageMath)

@CachedFunction

def A013989(n): return n+1 if (n<2) else (n+1)*(A013989(n-1) + n*A013989(n-2))/n

[denominator(A013989(n-1)/factorial(n)) for n in (1..30)] # G. C. Greubel, Aug 17 2022

Cf. A000085, A000142, A013989, A069943.

Sequence in context: A233283 A376247 A127918 * A253171 A073996 A003483

Adjacent sequences: A069941 A069942 A069943 * A069945 A069946 A069947

easy,frac,nonn

Benoit Cloitre, Apr 27 2002

approved