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.

0, 1, 1, 5, 17, 151, 823, 10631, 15871, 1344097, 12731713, 266731133, 3061359593, 15281334539, 1030023060151, 29833932429263, 461929309281059, 15229246883432833, 53257613193371021, 9845267571825141941, 191853269052081088769, 462422990938113014567, 168922073145947967975799

Offset: 0

Author

Terry D. Grant, May 05 2017

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 0..426

Crossrefs

Cf. A019609, A268363, A287596 (denominators).

Programs

Maple

R[0]:= 0: R[1]:= 1: A[0]:= 0: A[1]:= 1:
for n from 2 to 30 do
  R[n]:= R[n-1] + R[n-2]/(2*(n-1));
  A[n]:= numer(R[n]);
od:
seq(A[i],i=0..30); # Robert Israel, May 25 2017

Mathematica

Numerator[RecurrenceTable[{r[n] == r[n - 1] + r[n - 2]/(2 (n - 1)), r[0] == 0, r[1] == 1}, r, {n, 0, 25}]]

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

Formula

From Wolfdieter Lang, Jun 07 2017: (Start)

G.f. of {r(n)}_{n>=0}: x*exp(-x/2)/(1-x)^(3/2).

a(n) = numerator(r(n)). See the name for the recurrence of r(n). (End)

Extensions

Name changed, a(0) and a(1) added by David A. Corneth, May 14 2017

a(20)-a(22) from David A. Corneth, May 21 2017

Name corrected by Robert Israel, May 25 2017