|
Search: id:A082147
|
|
|
| A082147 |
|
a(0)=1, for n>=1 a(n)=sum(k=0,n,8^k*N(n,k)) where N(n,k) =1/n*C(n,k)*C(n,k+1) are the Narayana numbers (A001263). |
|
+0
7
|
|
| 1, 1, 9, 89, 945, 10577, 123129, 1476841, 18130401, 226739489, 2878666857, 37006326777, 480750990993, 6301611631473, 83240669582937, 1106980509493641, 14808497812637121, 199138509770855489, 2690461489090104009
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
More generally coefficients of (1+m*x-sqrt(m^2*x^2-(2*m+4)*x+1))/((2*m+2)*x) are given by : a(n)=sum(k=0,n,(m+1)^k*N(n,k))
The Hankel transform of this sequence is 8^C(n+1,2) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 29 2007
|
|
REFERENCES
|
Paul Barry, On Integer-Sequence-Based Constructions of Generalized Pascal Triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4.
|
|
FORMULA
|
G.f. (1+7*x-sqrt(49*x^2-18*x+1))/(16*x)
a(n) = Sum_{k=0..n} A088617(n, k)*8^k*(-7)^(n-k) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 21 2004
a(n) = [9(2n-1)a(n-1) - 49(n-2)a(n-2)] / (n+1) for n>=2, a(0) = a(1) = 1 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 19 2005
|
|
PROGRAM
|
(PARI) a(n)=if(n<1, 1, sum(k=0, n, 8^k/n*binomial(n, k)*binomial(n, k+1)))
|
|
CROSSREFS
|
Cf. A001003, A007564, A059231.
Sequence in context: A109002 A142991 A152267 this_sequence A095722 A069573 A101679
Adjacent sequences: A082144 A082145 A082146 this_sequence A082148 A082149 A082150
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Benoit Cloitre (benoit7848c(AT)orange.fr), May 10 2003
|
|
|
Search completed in 0.002 seconds
|
