|
| |
|
|
A081909
|
|
3^n(n^2-n+18)/18.
|
|
4
| |
|
|
1, 3, 10, 36, 135, 513, 1944, 7290, 26973, 98415, 354294, 1259712, 4428675, 15411789, 53144100, 181752822, 617003001, 2080591515, 6973568802, 23245229340, 77096677311, 254535261273, 836828256240, 2740612539186
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Binomial transform of A081908. 3rd binomial transform of (1,0,1,0,0,0,......). Case k=3 where a(n,k)=k^n(n^2-n+2k^2)/(2k^2) with G.f. (1-2kx+(k^2+1)x^2)/(1-kx)^3
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..185
|
|
|
FORMULA
| a(n)=3^n(n^2-n+18)/18 G.f.: (1-6x+10x^2)/(1-3x)^3
|
|
|
MATHEMATICA
| Table[3^n(n^2-n+18)/18, {n, 0, 30}] (* or *) CoefficientList[Series[ (1-6x+10x^2)/(1-3x)^3, {x, 0, 30}], x] (* From Harvey P. Dale, Apr 26 2011 *)
|
|
|
PROG
| (MAGMA) [3^n*(n^2-n+18)/18: n in [0..40]]; // Vincenzo Librandi, Apr 27 2011
|
|
|
CROSSREFS
| Cf. A081910.
Sequence in context: A102871 A119374 A126188 * A126189 A122448 A007582
Adjacent sequences: A081906 A081907 A081908 * A081910 A081911 A081912
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 31 2003
|
| |
|
|
