login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A034171 Related to triple factorial numbers A007559(n+1). 12
1, 6, 42, 315, 2457, 19656, 160056, 1320462, 11003850, 92432340, 781473420, 6642524070, 56716936290, 486145168200, 4180848446520, 36059817851235, 311811366125385, 2702365173086670, 23467908082068450, 204170800313995515 (list; graph; refs; listen; history; text; internal format)
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), #00.2.4.

Elżbieta Liszewska, Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019.

FORMULA

a(n) = 3^n*A007559(n+1)/(n+1)!, A007559(n+1)=(3*n+1)!!!; G.f.: (-1+(1-9*x)^(-1/3))/(3*x).

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

MATHEMATICA

CoefficientList[Series[(-1 + (1 - 9 x)^(-1/3))/(3 x), {x, 0, 19}], x] (* Michael De Vlieger, Oct 13 2019 *)

CROSSREFS

Cf. A007559, A034164. a(n)= A035529(n+1, 1) (first column of triangle).

Convolution of A004987(n) with A025748(n+1), n >= 0.

Cf. A298799, A004981, A004982.

Sequence in context: A093388 A162968 A247638 * A264911 A244902 A153293

Adjacent sequences:  A034168 A034169 A034170 * A034172 A034173 A034174

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 04:10 EST 2021. Contains 349530 sequences. (Running on oeis4.)