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 A108522 Number of increasing rooted trees with n generators. 5
 1, 2, 9, 70, 771, 10948, 190205, 3907494, 92654059, 2490459468, 74827519077, 2485153213814, 90403692195179, 3574835773247140, 152675377606343901, 7003761877546096278, 343454890456254782203, 17929588055863943650988 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A generator is a leaf or a node with just one child. In an increasing rooted tree, nodes are numbered and numbers increase as you move away from root. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 1..250 FORMULA E.g.f. satisfies: 2*A(x) = x - 1 + exp(A(x)) + Integral A(x) dx. - corrected by Vaclav Kotesovec and Paul D. Hanna, Mar 29 2014 From Paul D. Hanna, Mar 29 2014: (Start) E.g.f. satisfies: A(x) = A'(x)*(2 - exp(A(x))) - 1. E.g.f. satisfies: A'(x) = (1 + A(x))/(2 - exp(A(x)). (End) a(n) ~ c * n^(n-1) / (exp(n) * r^n), where r = 0.3160173586544089316502903103262192204293322854083... and c = 0.51723490785798357350192800634304... - Vaclav Kotesovec, Mar 29 2014 PROG (PARI) {a(n)=local(A=x); for(i=1, n, A=intformal((1+A)/(2-exp(A+x*O(x^n)))) ); n!*polcoeff(A, n)} for(n=1, 20, print1(a(n), ", ")) \\ Paul D. Hanna, Mar 29 2014 CROSSREFS Cf. A108521-A108529, A007151, A001147. Sequence in context: A201862 A167016 A300014 * A014500 A101482 A099717 Adjacent sequences:  A108519 A108520 A108521 * A108523 A108524 A108525 KEYWORD nonn AUTHOR Christian G. Bower, Jun 07 2005 STATUS approved

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Last modified October 23 08:40 EDT 2021. Contains 348211 sequences. (Running on oeis4.)