login
E.g.f. A(x) = 1 + Sum_{n>=1} (1/n!)*Product_{k=0..n-1} [exp(3^k*x) - 1].
1

%I #2 Mar 30 2012 18:37:07

%S 1,1,4,46,1519,145795,41134753,34354750885,85260288495316,

%T 630102185300832652,13884412839047621240875,

%U 912975607895806507921828357,179255108346123463104458490745825

%N E.g.f. A(x) = 1 + Sum_{n>=1} (1/n!)*Product_{k=0..n-1} [exp(3^k*x) - 1].

%e A(x) = 1 + x + 4x^2/2! + 46x^3/3! + 1519x^4/4! + 145795x^5/5! +...;

%e A(x) = 1 + [exp(x)-1] + [exp(x)-1][exp(3x)-1]/2! + [exp(x)-1][exp(3x)-1][exp(9x)-1]/3! + [exp(x)-1][exp(3x)-1][exp(9x)-1][exp(27x)-1]/4! +...

%o (PARI) {a(n)=n!*polcoeff(1+sum(j=1,n,(1/j!)*prod(k=0,j-1,1*exp(3^k*x)-1)),n)}

%Y Cf. variants: A135077, A135079.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 24 2007