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A118935 E.g.f.: A(x) = exp( Sum_{n>=0} x^(4^n)/4^((4^n-1)/3) ). 3

%I

%S 1,1,1,1,7,31,91,211,1681,12097,57961,209881,1874071,17842111,

%T 117303187,575683291,26124309121,412992394081,3670397429041,

%U 23161791013777,729420726627271,13374596287229311,143560108604864491

%N E.g.f.: A(x) = exp( Sum_{n>=0} x^(4^n)/4^((4^n-1)/3) ).

%C 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.

%F a(n) = Sum_{k=0..[n/4]} n!/[k!*(n-4*k)!*4^k] * a(k), with a(0)=1.

%e E.g.f. A(x) = exp( x + x^4/4 + x^16/4^5 + x^64/3^21 + x^256/3^85 +..)

%e = 1 + 1*x + 1*x^2/2! + 1*x^3/3! + 7*x^4/4! + 31*x^5/5!+ 91*x^6/6!+...

%o (PARI) a(n)=if(n==0,1,sum(k=0,n\4,n!/(k!*(n-4*k)!*4^k)*a(k)))

%o (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)

%Y Cf. A118933; variants: A118930, A118932.

%K nonn

%O 0,5

%A _Paul D. Hanna_, May 06 2006

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