A209923 E.g.f. A(x) satisfies: A( x - x^2/2 - Sum_{n>=3} (n-3)!*x^n/n! ) = x.

1, 1, 4, 26, 237, 2778, 39805, 674125, 13174189, 291802238, 7223963796, 197670359937, 5924155984714, 192988681624915, 6789966027406003, 256591956638230811, 10365414610788266136, 445744854494435066418, 20330276980162447348231, 980249560154126513379574

Offset: 1

Author

Paul D. Hanna, Mar 15 2012

Keywords

• nonn

Comments

Compare e.g.f. to the identity: let W(x) = Sum_{n>=1} (n-1)^(n-1)*x^n/n!, then W( x - Sum_{n>=1} x^(n+1)/(n*(n+1)) ) = x.

Examples

			E.g.f.: A(x) = x + x^2/2! + 4*x^3/3! + 26*x^4/4! + 237*x^5/5! +...
Let R(x) be the series reversion of e.g.f. A(x), then R(x) begins:
R(x) = x - x^2/(1*2) - x^3/(1*2*3) - x^4/(2*3*4) - x^5/(3*4*5) - x^6/(4*5*6) -...
		

Programs

PARI

{a(n)=n!*polcoeff(serreverse(x-x^2/2-sum(m=3,n,(m-3)!*x^m/m!) +x*O(x^n)),n)}
for(n=1,25,print1(a(n),", "))