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

0,3

Links

Table of n, a(n) for n=0..14.

Example

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! +...

Prog

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

Crossrefs

Cf. variants: A001831, A135078.

Sequence in context: A330764 A367487 A277355 * A157538 A024488 A217902

Adjacent sequences: A135074 A135075 A135076 * A135078 A135079 A135080

Keyword

nonn

Author

Paul D. Hanna, Nov 24 2007

Status

approved