|
| |
|
|
A123187
|
|
Triangle of coefficients in expansion of (1+13x)^n.
|
|
1
|
|
|
|
1, 1, 13, 1, 26, 169, 1, 39, 507, 2197, 1, 52, 1014, 8788, 28561, 1, 65, 1690, 21970, 142805, 371293, 1, 78, 2535, 43940, 428415, 2227758, 4826809, 1, 91, 3549, 76895, 999635, 7797153, 33787663, 62748517, 1, 104, 4732, 123032, 1999270, 20792408
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
LINKS
|
Table of n, a(n) for n=1..42.
|
|
|
FORMULA
|
p(k, x) = (13*x + 1)*p(k - 1, x)
T(n,k)=13^k*binomial(n,k)=sum_{i=n-k..n} binomial(i,n-k)*binomial(n,i)*12^(n-i). Row sums are 14^n = A001023. G.f.: 1 / [1 - x(1+13y)]. [From Mircea Merca, Apr 28 2012]
|
|
|
EXAMPLE
|
1
1, 13
1, 26, 169
1, 39, 507, 2197
1, 52, 1014, 8788, 28561
1, 65, 1690, 21970, 142805, 371293
|
|
|
MATHEMATICA
|
p[0, x] = 1; p[1, x] = 13*x + 1; p[k_, x_] := p[k, x] = (13*x + 1)*p[k - 1, x]; w = Table[CoefficientList[p[n, x], x], {n, 0, 10}]; Flatten[w]
|
|
|
CROSSREFS
|
Cf. A013609, A013610, A013611, A013621, A038220, A038222.
Sequence in context: A037283 A094709 A040181 * A046733 A120392 A133371
Adjacent sequences: A123184 A123185 A123186 * A123188 A123189 A123190
|
|
|
KEYWORD
|
nonn,tabl
|
|
|
AUTHOR
|
Roger L. Bagula and Gary W. Adamson, Oct 03 2006
|
|
|
STATUS
|
approved
|
| |
|
|
