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E.g.f.: 2 - exp(2) + Sum_{n>=1} 2^n * exp(3*x^n) / n!.
2

%I #7 Jun 20 2015 00:18:40

%S 1,6,30,78,426,582,12450,4758,407010,2218182,19172370,360438,

%T 4755166050,3213222,85631151090,5099958831318,54483404779650,

%U 258673542,11939347971403410,2326095798,5556296851712151330,35398724239897109862,10235928407592878130,188311523478,758680053859872239555010

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

%H Paul D. Hanna, <a href="/A258903/b258903.txt">Table of n, a(n) for n = 0..300</a>

%F E.g.f.: 2 - exp(3) + Sum_{n>=1} 3^n * exp(2*x^n) / n!.

%e E.g.f.: A(x) = 1 + 6*x + 30*x^2/2! + 78*x^3/3! + 426*x^4/4! + 582*x^5/5! +...

%e where

%e A(x) = 2 - exp(2) + 2*exp(3*x) + 2^2*exp(3*x^2)/2! + 2^3*exp(3*x^3)/3! + 2^4*exp(3*x^4)/4! + 2^5*exp(3*x^5)/5! +...

%e A(x) = 2 - exp(3) + 3*exp(2*x) + 3^2*exp(2*x^2)/2! + 3^3*exp(2*x^3)/3! + 3^4*exp(2*x^4)/4! + 3^5*exp(2*x^5)/5! +...

%o (PARI) {a(n) = local(A=1); A = 2-exp(2) + sum(m=1,n,2^m/m!*exp(3*x^m +x*O(x^n))); if(n==0,1, n!*polcoeff(A,n))}

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

%o (PARI) {a(n) = local(A=1); A = 2-exp(3) + sum(m=1,n,3^m/m!*exp(2*x^m +x*O(x^n))); if(n==0,1, n!*polcoeff(A,n))}

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

%Y Cf. A258899.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jun 20 2015