|
| |
|
|
A008548
|
|
Quintuple factorial numbers: product[ k=0..n-1 ] (5*k+1).
|
|
38
| |
|
|
1, 1, 6, 66, 1056, 22176, 576576, 17873856, 643458816, 26381811456, 1213563326976, 61891729675776, 3465936861843456, 211422148572450816, 13953861805781753856, 990724188210504523776, 75295038303998343806976
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| a(n), n>=1, enumerates increasing sextic (6-ary) trees with n vertices. W. Lang, Sept 14 2007.
Hankel transform is A169620. [From Paul Barry (pbarry(AT)wit.ie), Dec 03 2009]
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=0..50
W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
|
|
|
FORMULA
| E.g.f.: (1-5*x)^(-1/5).
a(n) ~ 2^(1/2)*pi^(1/2)*gamma(1/5)^-1*n^(-3/10)*5^n*e^-n*n^n*{1 + 1/300*n^-1 - ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001
a(n) = Sum_{k=0..n} (-5)^(n-k)*A048994(n, k) .- Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 29 2005
G.f.: 1/(1-x/(1-5x/(1-6x/(1-10x/(1-11x/(1-15x/(1-16x/(1-20x/(1-21x/(1-25x/(1-.../(1-A008851(n+1)*x/(1-... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Dec 03 2009]
|
|
|
MAPLE
| f := n->product( (5*k+1), k=0..(n-1));
restart: G(x):=(1-5*x)^(-1/5): f[0]:=G(x): for n from 1 to 29 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..16); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 03 2009]
|
|
|
MATHEMATICA
| s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 5, 5!, 5}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 08 2008]
Table[Product[5k+1, {k, 0, n-1}], {n, 0, 20}] (* From Harvey P. Dale, Apr 23 2011 *)
FoldList[Times, 1, NestList[#+5&, 1, 20]] (*Chandler*)
|
|
|
PROG
| (Pari) x='x+O('x^33); /* that many terms */
Vec(serlaplace((1-5*x)^(-1/5))) /* show terms */ /* Joerg Arndt, Apr 24 2011 */
|
|
|
CROSSREFS
| Cf. A001147, A007559, A007696, A016861, A034687, A034688, A052562, A047055, A051150.
a(n)= A049385(n, 1) (first column of triangle).
Sequence in context: A169715 A128319 A174496 * A090358 A112942 A113390
Adjacent sequences: A008545 A008546 A008547 * A008549 A008550 A008551
|
|
|
KEYWORD
| nonn,nice,easy
|
|
|
AUTHOR
| Joe Keane (jgk(AT)jgk.org)
|
| |
|
|
