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 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. 3
 1, 1, 2, 8, 74, 2122, 267292, 194323504, 980945301116, 39560543100700028, 14356125485861852659544, 52095666080476161483596777824, 2079492908949143825845786572097662328, 996080457608702027557335524810508733871848312 (list; graph; refs; listen; history; text; internal format)
 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 LINKS 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 Cf. A274760, A007548, A275593, A275594. Sequence in context: A143760 A064605 A295373 * A204552 A002668 A193205 Adjacent sequences:  A132036 A132037 A132038 * A132040 A132041 A132042 KEYWORD nonn,eigen AUTHOR Paul D. Hanna, Aug 07 2007 STATUS approved

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Last modified June 17 17:12 EDT 2019. Contains 324196 sequences. (Running on oeis4.)