OFFSET
0,2
COMMENTS
Working with an offset of 1, we conjecture a(p*n) = a(n) (mod p^2) for prime p = 1 (mod 3) and all positive integers n except those n of the form n = m*p + k for 0 <= m <= (p-1)/3 and 1 <= k <= (p-1)/3. Cf. A298799, A004981 and A004982. - Peter Bala, Dec 23 2019
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..1050
Wolfdieter Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), Article 00.2.4.
Elżbieta Liszewska and Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019.
FORMULA
G.f.: (-1+(1-9*x)^(-1/3))/(3*x).
a(n)= A035529(n+1, 1) (first column of triangle).
D-finite with recurrence: (n+1)*a(n) +3*(-3*n-1)*a(n-1)=0. - R. J. Mathar, Jan 28 2020
G.f.: (1F0(1/3;;9*x)-1)/(3*x). - R. J. Mathar, Jan 28 2020
Sum_{n>=0} 1/a(n) = 3/8 + 3*sqrt(3)*Pi/32 + 9*log(3)/32. - Amiram Eldar, Dec 22 2022
MATHEMATICA
CoefficientList[Series[(-1 + (1 - 9 x)^(-1/3))/(3 x), {x, 0, 19}], x] (* Michael De Vlieger, Oct 13 2019 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved