|
Search: id:A158843
|
|
| |
|
| 1, 2, 20, 952, 336112, 742166496, 10043945021760, 814531629739559808, 393150002983518264270592, 1123538097532735360702239462912, 18948231465474675384343860006353603584
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Compare to g.f.: exp( Sum_{n>=1} 2*A001333(n)*x^n/n ) = 1/(1-2*x-x^2), which is the g.f. of the Pell numbers A000129 (with offset), where A001333(n) = A000129(n+1) - A000129(n).
|
|
EXAMPLE
|
G.f.: A(x) = 1 + 2*x + 20*x^2 + 952*x^3 + 336112*x^4 + 742166496*x^5 +...
log(A(x)) = 2*x + 6^2*x^2/2 + 14^3*x^3/3 + 34^4*x^4/4 + 82^5*x^5/5 +...
log(G(x)) = 2*x + 6*x^2/2 + 14*x^3/3 + 34*x^4/4 + 82*x^5/5 +...
G(x) = 1 + 2*x + 5*x^2 + 12*x^3 + 29*x^4 + 70*x^5 + 169*x^6 +... (A000129).
|
|
PROGRAM
|
(PARI) {a(n)=local(LD=Vec(2*(1+x)/(1-2*x-x^2 +x*O(x^n)))); polcoeff(exp(sum(m=1, n, LD[m]^m*x^m/m)+x*O(x^n)), n)}
|
|
CROSSREFS
|
Cf. A000129, A001333.
Sequence in context: A013148 A006547 A135757 this_sequence A008793 A015192 A012790
Adjacent sequences: A158840 A158841 A158842 this_sequence A158844 A158845 A158846
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Apr 09 2009
|
|
|
Search completed in 0.002 seconds
|
