A058956 Let S(t) = 1 + s_1*t + s_2*t^2 + ... satisfy S' = -S/(2 + S); sequence gives denominators of s_n.

1, 3, 27, 1, 4374, 98415, 885735, 3720087, 55801305, 1291401630, 813583026900, 4027235983155, 724902476967900, 7710326345931300, 5343256157730390900, 52845390570959910, 5770716650348822172000, 441459823751684896158000

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

S(t) = 2*LambertW((1/2)*exp(-(1/2)*t)*exp(1/2)).

Example

S(t) = 1-1/3*t+1/27*t^2-1/4374*t^4-1/98415*t^5+...

Mathematica

m = 17; S[t_] = Sum[s[k] t^k, {k, 0, m}]; s[0] = 1;
sol = Solve[Thread[CoefficientList[S'[t] + S[t]/(2+S[t])+O[t]^m, t] == 0]];
s /@ Range[0, m] /. sol[[1]] // Denominator (* Jean-François Alcover, Oct 01 2019 *)

Crossrefs

Cf. A058955.

Sequence in context: A214808 A219895 A088730 * A010257 A334567 A284863

Adjacent sequences: A058953 A058954 A058955 * A058957 A058958 A058959

Keyword

nonn,frac

Author

N. J. A. Sloane, Jan 13 2001

Status

approved