A249479 E.g.f.: Sum_{n>=0} x^n / Product_{k=1..n} (k - x^k).

1, 1, 3, 10, 47, 246, 1622, 11656, 97869, 899338, 9225674, 102689808, 1252353159, 16392179766, 231501723312, 3489107989204, 56102882993753, 956324067974034, 17265334914237406, 328565326494695912, 6582472704969812115, 138369486361447809150, 3047029944703252620540, 70122393369209990745660

Offset: 0

Author

Paul D. Hanna, Oct 29 2014

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 3*x^2/2! + 10*x^3/3! + 47*x^4/4! + 246*x^5/5! +...
where
A(x) = 1 + x/(1-x) + x^2/((1-x)*(2-x^2)) + x^3/((1-x)*(2-x^2)*(3-x^3)) + x^4/((1-x)*(2-x^2)*(3-x^3)*(4-x^4)) + x^5/((1-x)*(2-x^2)*(3-x^3)*(4-x^4)*(5-x^5)) +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A007841, A249480.

Programs

PARI

{a(n)=local(A=1);A=sum(m=0,n,x^m/prod(k=1,m,k-x^k +x*O(x^n)));n!*polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))

Formula

a(n) ~ exp(1) * n!. - Vaclav Kotesovec, Nov 01 2014