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A286307 a(n) is the numerator of r(n), where r(n) = r(n-1) + r(n-2)/(2*(n-1)) with r(0) = 0, r(1) = 1.

%I A286307 #34 Jul 08 2025 08:48:27
%S A286307 0,1,1,5,17,151,823,10631,15871,1344097,12731713,266731133,3061359593,
%T A286307 15281334539,1030023060151,29833932429263,461929309281059,
%U A286307 15229246883432833,53257613193371021,9845267571825141941,191853269052081088769,462422990938113014567,168922073145947967975799
%N A286307 a(n) is the numerator of r(n), where r(n) = r(n-1) + r(n-2)/(2*(n-1)) with r(0) = 0, r(1) = 1.
%H A286307 Robert Israel, <a href="/A286307/b286307.txt">Table of n, a(n) for n = 0..426</a>
%F A286307 From _Wolfdieter Lang_, Jun 07 2017: (Start)
%F A286307 G.f. of {r(n)}_{n>=0}: x*exp(-x/2)/(1-x)^(3/2).
%F A286307 a(n) = numerator(r(n)). See the name for the recurrence of r(n). (End)
%p A286307 R[0]:= 0: R[1]:= 1: A[0]:= 0: A[1]:= 1:
%p A286307 for n from 2 to 30 do
%p A286307   R[n]:= R[n-1] + R[n-2]/(2*(n-1));
%p A286307   A[n]:= numer(R[n]);
%p A286307 od:
%p A286307 seq(A[i],i=0..30); # _Robert Israel_, May 25 2017
%t A286307 Numerator[RecurrenceTable[{r[n] == r[n - 1] + r[n - 2]/(2 (n - 1)), r[0] == 0, r[1] == 1}, r, {n, 0, 25}]]
%o A286307 (PARI) a(n) = if(n < 2, return(n)); n++; my(v=vector(n)); v[1]=0; v[2] = 1; for(i = 3, n, v[i] = v[i-1] + v[i-2]/(2*i - 4)); numerator(v[#v]) \\ _David A. Corneth_, May 14 2017
%Y A286307 Cf. A019609, A268363, A287596 (denominators).
%K A286307 nonn,easy
%O A286307 0,4
%A A286307 _Terry D. Grant_, May 05 2017
%E A286307 Name changed, a(0) and a(1) added by _David A. Corneth_, May 14 2017
%E A286307 a(20)-a(22) from _David A. Corneth_, May 21 2017
%E A286307 Name corrected by _Robert Israel_, May 25 2017