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 A177779 E.g.f.: A(x) = Sum_{n>=0} (1/n!)*Product_{k=0..n-1} L(3^k*x), where L(x) is the e.g.f. of A177780. 1

%I #2 Mar 30 2012 18:37:22

%S 1,1,7,159,10065,1769889,892392183,1321983917631,5822841033057825,

%T 76645599313018616001,3021493143896197748386407,

%U 357064253282406274455859700319,126544129732367263008235662373092465

%N E.g.f.: A(x) = Sum_{n>=0} (1/n!)*Product_{k=0..n-1} L(3^k*x), where L(x) is the e.g.f. of A177780.

%e E.g.f.: A(x) = 1 + x + 7*x^2/2! + 159*x^3/3! + 10065*x^4/4! +...

%e Then e.g.f. A(x) is given by:

%e A(x) = 1 + L(x) + L(x)L(3x)/2! + L(x)L(3x)L(9x)/3! + L(x)L(3x)L(9x)L(27x)/4! +...

%e where L(x) is the e.g.f. of A177780:

%e . L(x) = x + 4*x^2/2! + 60*x^3/3! + 2496*x^4/4! + 276240*x^5/5! +...

%e . L(x) = x*d/dx log( Sum_{n>=0} 3^(n(n-1)/2)*x^n/n! )

%e and satisfies:

%e . L(x)/x = 1 + 2*L(x) + 2^2*L(x)L(3x)/2! + 2^3*L(x)L(3x)L(9x)/3! + 2^4*L(x)L(3x)L(9x)L(27x)/4! +...

%o (PARI) {a(n,q=3)=local(Lq=x+x^2,A); for(i=1,n,Lq=x*sum(m=0,n,(q-1)^m/m!*prod(k=0,m-1,subst(Lq,x,q^k*x+x*O(x^n))))); A=sum(m=0,n,1/m!*prod(k=0,m-1,subst(Lq,x,q^k*x+x*O(x^n))));n!*polcoeff(A,n)}

%Y Cf. A177780.

%K nonn

%O 0,3

%A _Paul D. Hanna_, May 20 2010

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Last modified May 31 17:17 EDT 2023. Contains 363068 sequences. (Running on oeis4.)