A285381 G.f.: 1/(1 - 1!*x/(1 - 2!*x^2/(1 - 3!*x^3/(1 - 4!*x^4/(1 - 5!*x^5/(1 - 6!*x^6/(1 - ...))))))), a continued fraction.

1, 1, 1, 3, 5, 11, 33, 67, 169, 435, 1265, 3035, 8025, 22243, 60721, 191307, 491657, 1404371, 4089633, 12183835, 36872377, 126189219, 350136977, 1062359147, 3386475177, 10757830387, 36121721857, 120817807419, 482847966617, 1391650703939, 4654331013489

Offset: 0

Author

Ilya Gutkovskiy, Apr 17 2017

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 5*x^4 + 11*x^5 + 33*x^6 + 67*x^7 + 169*x^8 + ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A000142, A088357, A285380.

Programs

Mathematica

nmax = 30; CoefficientList[Series[1/(1 + ContinuedFractionK[-k! x^k, 1, {k, 1, nmax}]), {x, 0, nmax}], x]

PARI

a(n) = my(A=1+O(x)); for(i=1, n, A=1-(n-i+1)!*x^(n-i+1)/A); polcoef(1/A, n); \\ Seiichi Manyama, Apr 16 2021