|
| |
|
|
A053108
|
|
Expansion of 1/(1-9*x)^9.
|
|
4
|
|
|
|
1, 81, 3645, 120285, 3247695, 75996063, 1595917323, 30778405515, 554011299270, 9418192087590, 152574711818958, 2371843247367438, 35577648710511570, 517244277406668210, 7315311923322878970
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 0..400
|
|
|
FORMULA
|
a(n) = 9^n*binomial(n+8, 8). G.f.: 1/(1-9*x)^9.
a(0)=1, a(1)=81, a(2)=3645, a(3)=120285, a(4)=3247695, a(5)=75996063, a(6)=1595917323, a(7)=30778405515, a(8)=554011299270, a(n)=81*a(n-1) -2916*a(n-2) +61236*a(n-3) -826686*a(n-4) +7440174*a(n-5) -44641044*a(n-6) +172186884*a(n-7) -387420489*a(n-8) +387420489*a(n-9). [From Harvey P. Dale, Jan 21 2012]
|
|
|
MATHEMATICA
|
CoefficientList[Series[1/(1-9x)^9, {x, 0, 30}], x] (* From Harvey P. Dale, Jan 21 2012 *)
|
|
|
PROG
|
(Sage)[lucas_number2(n, 9, 0)*binomial(n, 8)/9^8 for n in xrange(8, 23)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 13 2009]
(MAGMA) [Binomial(n+8, 8)*9^n: n in [0..20]]; // Vincenzo Librandi, Oct 13 2011
|
|
|
CROSSREFS
|
Cf. A053107.
Sequence in context: A017744 A223477 A223501 * A016888 A205238 A006312
Adjacent sequences: A053105 A053106 A053107 * A053109 A053110 A053111
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Wolfdieter Lang
|
|
|
STATUS
|
approved
|
| |
|
|
