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A069944 a(n) = denominator(b(n)), where b(1) = b(2) = 1, b(n) = (b(n-1) + b(n-2))/(n-1). 3
1, 1, 1, 3, 12, 60, 180, 630, 10080, 18144, 453600, 2494800, 59875200, 778377600, 1089728640, 40864824000, 1307674368000, 22230464256000, 15390321408000, 380140938777600, 76028187755520000, 1596591942865920000 (list; graph; refs; listen; history; text; internal format)
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
FORMULA
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
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:= 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
CROSSREFS
Sequence in context: A090830 A233283 A127918 * A253171 A073996 A003483
KEYWORD
easy,frac,nonn
AUTHOR
Benoit Cloitre, Apr 27 2002
STATUS
approved

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Last modified June 12 16:34 EDT 2024. Contains 373334 sequences. (Running on oeis4.)