OFFSET
0,3
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
FORMULA
a(n+1) = Sum_{k=0..n} n!/k!*a(k)*a(n-k). - Vladeta Jovovic, Jul 08 2008
EXAMPLE
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 +...) .
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
PROG
(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))}
CROSSREFS
KEYWORD
nonn,eigen
AUTHOR
Paul D. Hanna, Aug 07 2007
STATUS
approved