A199670 E.g.f.: d/dx Series_Reversion( Sum_{n>=0} (-x)^(3*n)/(3*n)! - exp(-x) ).

1, 1, 3, 16, 119, 1134, 13201, 181594, 2882061, 51836302, 1041959555, 23148374886, 563234624575, 14895783741202, 425457081218169, 13052033357204842, 428016906877603589, 14941465218939490686, 553193807213161191259, 21651761774465075118502, 893244763931287659927399

Offset: 0

Author

Paul D. Hanna, Nov 08 2011

Keywords

• nonn

Comments

Compare to e.g.f. F(x) of A183611, which satisfies F'(x) = F(x)^2 + x*F(x)^3, where F(x) = d/dx Series_Reversion( Sum_{n>=1} x^(3*n-2)/(3*n-2)! - x^(3*n-1)/(3*n-1)! ).

Examples

			E.g.f.: A(x) = 1 + x + 3*x^2/2! + 16*x^3/3! + 119*x^4/4! + 1134*x^5/5! +...
E.g.f.: A(x) = d/dx Series_Reversion(G(x)) where G(x) begins:
G(x) = x - x^2/2! - x^4/4! + x^5/5! + x^7/7! - x^8/8! - x^10/10! + x^11/11! +...
The series reversion of G(x) begins:
x + x^2/2! + 3*x^3/3! + 16*x^4/4! + 119*x^5/5! + 1134*x^6/6! +...
		

Crossrefs

Cf. A183611, A199675.

Programs

PARI

{a(n)=n!*polcoeff(deriv(serreverse(sum(m=0, n\3+1, (-x)^(3*m)/(3*m)!)-exp(-x+x^2*O(x^n)))), n)}

PARI

{a(n)=n!*polcoeff(deriv(serreverse(sum(m=1, n\3+1, -(-x)^(3*m-2)/(3*m-2)!-(-x)^(3*m-1)/(3*m-1)!+x^2*O(x^n)))), n)}