|
Search: id:A082305
|
|
|
| A082305 |
|
G.f.: (1-6*x-sqrt(36*x^2-16*x+1))/(2*x). |
|
+0
6
|
|
| 1, 7, 56, 497, 4760, 48174, 507696, 5516133, 61363736, 695540258, 8004487568, 93283238986, 1098653880688, 13056472392796, 156371970692448, 1885491757551213, 22870028390806296, 278862330338622618
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
More generally coefficients of (1-m*x-sqrt(m^2*x^2-(2*m+4)*x+1))/(2*x) are given by a(0)=1 and n>0 a(n)=(1/n)*sum(k=0,n,(m+1)^k*C(n,k)*C(n,k-1))
|
|
REFERENCES
|
Paul Barry, On Integer-Sequence-Based Constructions of Generalized Pascal Triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4.
|
|
FORMULA
|
a(0)=1, n>0 a(n)=(1/n)*sum(k=0, n, 7^k*C(n, k)*C(n, k-1))
|
|
PROGRAM
|
(PARI) a(n)=if(n<1, 1, sum(k=0, n, 7^k*binomial(n, k)*binomial(n, k-1))/n)
|
|
CROSSREFS
|
Cf. A006318, A047891.
Sequence in context: A055274 A126694 A024091 this_sequence A001730 A087751 A099345
Adjacent sequences: A082302 A082303 A082304 this_sequence A082306 A082307 A082308
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Benoit Cloitre (benoit7848c(AT)orange.fr), May 10 2003
|
|
|
Search completed in 0.002 seconds
|
