A132039 E.g.f.: A(x) = Sum_{n>=0} a(n)*x^n/n! = exp( Sum_{n>=0} a(n)*x^(n+1)/(n+1) ) with a(0) = 1.

1, 1, 2, 8, 74, 2122, 267292, 194323504, 980945301116, 39560543100700028, 14356125485861852659544, 52095666080476161483596777824, 2079492908949143825845786572097662328, 996080457608702027557335524810508733871848312

Offset: 0

Author

Paul D. Hanna, Aug 07 2007

Keywords

• nonn
• eigen

Comments

Shifts A132039(n-1), n >= 1, one place left under MNL transform, see A274760. Pointed out by Paul D. Hanna. - Johannes W. Meijer, Aug 03 2016

Examples

			E.g.f.: A(x) = 1 + 1*x + 2*x^2/2! + 8*x^3/3! + 74*x^4/4! + 2122*x^5/5! +...;
E.g.f.: A(x) = exp(x + 1*x^2/2 + 2*x^3/3 + 8*x^4/4 + 74*x^5/5 + 2122*x^6/6 +...) .
		

Crossrefs

Cf. A274760, A007548, A275593, A275594.

Programs

Maple

A132039 := proc(n) option remember: if n=0 then 1 else add((n-1)!/k!*A132039(k)*A132039(n-1-k),k=0..n-1) fi: end: seq(A132039(n), n=0..13);
nmax:=13: t1 := add(a(n)*x^n/n!, n=0..nmax): t2 := series(exp(add(a(n)*x^(n+1)/(n+1), n=0..nmax)), x, nmax+1): a(0) := 1: for n from 1 to nmax do a(n) := n!*coeff(t2, x, n) od: A132039 := proc(n): a(n) end: seq(A132039(n), n=0..nmax); # Johannes W. Meijer, Aug 03 2016

PARI

{a(n)=if(n==0,1,n!*polcoeff(exp(sum(k=0,n-1,a(k)*x^(k+1)/(k+1))+x^2*O(x^n)),n))}

Formula

a(n+1) = Sum_{k=0..n} n!/k!*a(k)*a(n-k). - Vladeta Jovovic, Jul 08 2008