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A118932 E.g.f.: A(x) = exp( Sum_{n>=0} x^(3^n)/3^((3^n-1)/2) ). 4

%I

%S 1,1,1,3,9,21,81,351,1233,10249,75841,388411,3733401,33702813,

%T 215375889,1984583511,19181083041,141963117201,1797976123393,

%U 22534941675379,202605151063081,2992764505338021,43182110678814801,445326641624332623

%N E.g.f.: A(x) = exp( Sum_{n>=0} x^(3^n)/3^((3^n-1)/2) ).

%C Equals invariant column vector V that satisfies matrix product A118931*V = V, where A118931(n,k) = n!/[k!(n-3k)!*3^k] for n>=3*k>=0; thus a(n) = Sum_{k=0..[n/3]} A118931(n,k)*a(k), with a(0)=1.

%F a(n) = Sum_{k=0..[n/3]} n!/[k!*(n-3*k)!*3^k] * a(k), with a(0)=1.

%e E.g.f. A(x) = exp( x + x^3/3 + x^9/3^4 + x^27/3^13 + x^81/3^40 +...)

%e = 1 + 1*x + 1*x^2/2! + 3*x^3/3! + 9*x^4/4! + 21*x^5/5!+ 81*x^6/6!+...

%o (PARI) {a(n) = if(n==0,1,sum(k=0,n\3,n!/(k!*(n-3*k)!*3^k)*a(k)))}

%o for(n=0,30,print1(a(n),", "))

%o (PARI) /* Defined by E.G.F.: */

%o {a(n) = n!*polcoeff( exp(sum(k=0,ceil(log(n+1)/log(3)),x^(3^k)/3^((3^k-1)/2))+x*O(x^n)),n,x)}

%o for(n=0,30,print1(a(n),", "))

%Y Cf. A118931; variants: A118930, A118935.

%K nonn

%O 0,4

%A _Paul D. Hanna_, May 06 2006

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Last modified July 4 14:15 EDT 2020. Contains 335448 sequences. (Running on oeis4.)