A207649 E.g.f.: Sum_{n>=0} 1/n! * Product_{k=1..n} ((1+x)^k - 1).

1, 1, 2, 9, 60, 580, 7380, 119700, 2387280, 57211056, 1615703040, 52950688560, 1988213895360, 84622184412480, 4045503794492160, 215531680987022400, 12709328457015590400, 824497514996060505600, 58531734588587835294720, 4525412571041289046479360, 379428698362674642409728000, 34365923697307101211784908800, 3350637193653655199937586944000

Offset: 0

Author

Paul D. Hanna, Feb 19 2012

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 2*x^2/2! + 9*x^3/3! + 60*x^4/4! + 580*x^5/5! +...
such that, by definition,
A(x) = 1 + ((1+x)-1) + ((1+x)-1)*((1+x)^2-1)/2! + ((1+x)-1)*((1+x)^2-1)*((1+x)^3-1)/3! + ((1+x)-1)*((1+x)^2-1)*((1+x)^3-1)*((1+x)^4-1)/4! +...
or, more explicitly,
A(x) = 1 + x + x^2*(2+x)/2! + x^3*(2+x)*(3+3*x+x^2)/3! + x^4*(2+x)*(3+3*x+x^2)*(4+6*x+4*x^2+x^3)/4! + x^5*(2+x)*(3+3*x+x^2)*(4+6*x+4*x^2+x^3)*(5+10*x+10*x^2+5*x^3+x^4)/5! +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A179525.

Programs

PARI

{a(n)=n!*polcoeff(sum(m=0,n,1/m!*prod(k=1,m,(1+x)^k-1 +x*O(x^n)) ),n)}
for(n=0,25,print1(a(n),", "))

Extensions

a(21)-a(22) corrected by Andrew Howroyd, Feb 22 2018