A187803 E.g.f.: Sum_{n>=0} Product_{k=1..n} (1 - exp(-n*k*x)).

1, 1, 15, 829, 113487, 31137061, 15015039495, 11636995485949, 13584094722071007, 22735343245138118101, 52487807127760090483575, 162018777092079952134169069, 651747862300297714019151918927, 3344015911143306355676226376118341, 21488215819992049616143504500848490855

Offset: 0

Author

Paul D. Hanna, Jan 06 2013

Keywords

• nonn

Comments

Compare to the e.g.f. of A079144, enumerating certain labeled interval orders:

Sum_{n>=0} Product_{k=1..n} (1 - exp(-k*x)).

Also compare to the e.g.f. of A220181: Sum_{n>=0} (1 - exp(-n*x))^n.

Examples

			E.g.f.: A(x) = 1 + x + 15*x^2/2! + 829*x^3/3! + 113487*x^4/4! +...
where
A(x) = 1 + (1-exp(-x)) + (1-exp(-2*1*x))*(1-exp(-2*2*x)) + (1-exp(-3*1*x))*(1-exp(-3*2*x))*(1-exp(-3*3*x)) + (1-exp(-4*1*x))*(1-exp(-4*2*x))*(1-exp(-4*3*x))*(1-exp(-4*4*x)) +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..140

Crossrefs

Cf. A079144, A220181.

Programs

PARI

{a(n)=n!*polcoeff(sum(m=0, n, prod(k=1,m,(1-exp(-m*k*x+x*O(x^n)))) ), n)}
for(n=0, 20, print1(a(n), ", "))

Formula

a(n) ~ c * d^n * (n!)^3 / sqrt(n), where d = 2.426663845780394275167988381..., c = 0.504146101604802096078745... . - Vaclav Kotesovec, Nov 03 2014