A135077 - OEIS

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

%S 1,1,3,18,209,4650,198933,16482902,2663887921,844592892082,

%T 527562202908045,651188478953301102,1591732149339598508105,

%U 7716508793733513473433162,74274446413528969422741614565

%N E.g.f. A(x) = 1 + Sum_{n>=1} (1/n!)*Product_{k=0..n-1} [exp(2^k*x) - 1].

%e E.g.f.: A(x) = 1 + x + 3x^2/2! + 18x^3/3! + 209x^4/4! + 4650x^5/5! +...;

%e A(x) = 1 + [exp(x)-1] + [exp(x)-1][exp(2x)-1]/2! + [exp(x)-1][exp(2x)-1][exp(4x)-1]/3! + [exp(x)-1][exp(2x)-1][exp(4x)-1][exp(8x)-1]/4! +...

%o (PARI) {a(n)=n!*polcoeff(1+sum(j=1,n,(1/j!)*prod(k=0,j-1,1*exp(2^k*x)-1)),n)}

%Y Cf. variants: A001831, A135078.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 24 2007