|
Search: id:A155205
|
|
|
| A155205 |
|
G.f.: A(x) = exp( Sum_{n>=1} (3^n - 1)^n * x^n/n ), a power series in x with integer coefficients. |
|
+0
7
|
|
| 1, 2, 34, 5924, 10252294, 166020197708, 24810918565918804, 34076399079565985138408, 428687477154543524080261047622, 49247086840315416213775472777558582540
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
More generally, for m integer, exp( Sum_{n>=1} (m^n + y)^n * x^n/n ) is a power series in x and y with integer coefficients.
|
|
EXAMPLE
|
G.f.: A(x) = 1 + 2*x + 34*x^2 + 5924*x^3 + 10252294*x^4 +...
log(A(x)) = 2*x + 8^2*x^2/2 + 26^3*x^3/3 + 80^4*x^4/4 + 242^5*x^5/5 +...
|
|
PROGRAM
|
(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, (3^m-1)^m*x^m/m)+x*O(x^n)), n)}
|
|
CROSSREFS
|
Cf. A155203, A155204, A155206, A155812 (triangle), variants: A155202, A155209.
Sequence in context: A134495 A165938 A002782 this_sequence A045529 A077747 A041012
Adjacent sequences: A155202 A155203 A155204 this_sequence A155206 A155207 A155208
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Feb 04 2009
|
|
|
Search completed in 0.002 seconds
|
