The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 G. C. Greubel, Table of n, a(n) for n = 1..350 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 Cf. A000085, A000142, A013989, A069943. Sequence in context: A090830 A233283 A127918 * A253171 A073996 A003483 Adjacent sequences: A069941 A069942 A069943 * A069945 A069946 A069947 KEYWORD easy,frac,nonn AUTHOR Benoit Cloitre, Apr 27 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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