A135077 E.g.f. A(x) = 1 + Sum_{n>=1} (1/n!)*Product_{k=0..n-1} [exp(2^k*x) - 1].
1, 1, 3, 18, 209, 4650, 198933, 16482902, 2663887921, 844592892082, 527562202908045, 651188478953301102, 1591732149339598508105, 7716508793733513473433162, 74274446413528969422741614565
Offset: 0
Keywords
Examples
E.g.f.: A(x) = 1 + x + 3x^2/2! + 18x^3/3! + 209x^4/4! + 4650x^5/5! +...; 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! +...
Programs
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PARI
{a(n)=n!*polcoeff(1+sum(j=1,n,(1/j!)*prod(k=0,j-1,1*exp(2^k*x)-1)),n)}