|
Search: id:A118396
|
|
|
| A118396 |
|
Eigenvector of triangle A118394; E.g.f.: exp( Sum_{n>=0} x^(3^n) ). |
|
+0
3
|
|
| 1, 1, 1, 7, 25, 61, 481, 2731, 10417, 454105, 4309921, 23452111, 592433161, 6789801877, 46254009985, 893881991731, 11548704851041, 93501748795441, 4828847934591937, 83867376656907415, 823025819684123641
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
E.g.f. of triangle A118394 is: exp(x+y*x^3), where A118394(n,k) = n!/k!/(n-3*k)!. More generally, given a triangle with e.g.f.: exp(x+y*x^b), the eigenvector will have e.g.f.: exp( Sum_{n>=0} x^(b^n) ).
|
|
FORMULA
|
a(n) = Sum_{k=0..[n/3]} n!/k!/(n-3*k)! *a(k) for n>=0, with a(0)=1.
|
|
PROGRAM
|
(PARI) {a(n)=n!*polcoeff(exp(sum(k=0, ceil(log(n+1)/log(3)), x^(3^k))+x*O(x^n)), n)}
|
|
CROSSREFS
|
Cf. A118394, A118395; variants: A118393, A118932.
Sequence in context: A098538 A033814 A118395 this_sequence A001845 A127765 A155305
Adjacent sequences: A118393 A118394 A118395 this_sequence A118397 A118398 A118399
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), May 07 2006
|
|
|
Search completed in 0.002 seconds
|
