|
Search: id:A118935
|
|
|
| A118935 |
|
E.g.f.: A(x) = exp( Sum_{n>=0} x^(4^n)/4^((4^n-1)/3) ). |
|
+0
4
|
|
| 1, 1, 1, 1, 7, 31, 91, 211, 1681, 12097, 57961, 209881, 1874071, 17842111, 117303187, 575683291, 26124309121, 412992394081, 3670397429041, 23161791013777, 729420726627271, 13374596287229311, 143560108604864491
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
Equals invariant column vector V that satisfies matrix product A118933*V = V, where A118933(n,k) = n!/[k!(n-4k)!*4^k] for n>=4*k>=0; thus a(n) = Sum_{k=0..[n/4]} A118933(n,k)*a(k), with a(0)=1.
|
|
FORMULA
|
a(n) = Sum_{k=0..[n/4]} n!/[k!*(n-4*k)!*4^k] * a(k), with a(0)=1.
|
|
EXAMPLE
|
E.g.f. A(x) = exp( x + x^4/4 + x^16/4^5 + x^64/3^21 + x^256/3^85 +..)
= 1 + 1*x + 1*x^2/2! + 1*x^3/3! + 7*x^4/4! + 31*x^5/5!+ 91*x^6/6!+...
|
|
PROGRAM
|
(PARI) {a(n)=if(n==0, 1, sum(k=0, n\4, n!/(k!*(n-4*k)!*4^k)*a(k)))} (PARI) /* Defined by E.G.F.: */ {a(n)=n!*polcoeff( exp(sum(k=0, ceil(log(n+1)/log(4)), x^(4^k)/4^((4^k-1)/3))+x*O(x^n)), n, x)}
|
|
CROSSREFS
|
Cf. A118933; variants: A118930, A118932.
Sequence in context: A107006 A107005 A118934 this_sequence A055899 A139876 A107392
Adjacent sequences: A118932 A118933 A118934 this_sequence A118936 A118937 A118938
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), May 06 2006
|
|
|
Search completed in 0.002 seconds
|
