A248099 - OEIS

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A248099

Number of ordered trees with root degree n and having strictly thinning limbs. An ordered tree with strictly thinning limbs is such that if a node has k children, each of its children has less than k children.

1, 4, 216, 2428912656, 84539502447168140812774402430429967453919558368 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,2`
	COMMENTS	`The next term is too large to include (282 digits).` `First differences of A110387.`
	LINKS	`Table of n, a(n) for n=1..5.`
	FORMULA	`a(1)=1; a(n) = (1 + a(1) + ... + a(n-1))^n for n>=2.` `a(1)=1; a(n) = (a(n-1)^{1/(n-1)} + a(n-1))^n for n>=2.` `For the g.f. F[n](z) of the ordered trees with root degree n and having strictly thinning limbs, where z marks number of vertices, we have F[1](z) = z^2 and F[n] = z*(F[n-1] + (F[n-1]/z)^{1/(n-1)})^n for n>=2.`
	EXAMPLE	`a(2)=4; indeed, we have /\ and the 3 trees obtained by hanging \| to either of the leaves of /\ or to both of them.`
	MAPLE	`a[1] := 1: for n from 2 to 6 do a[n] := simplify((a[n-1]^(1/(n-1))+a[n-1])^n) end do: seq(a[n], n = 1 .. 6);`
	CROSSREFS	`Cf. A110387.` `Sequence in context: A038786 A268362 A072694 * A068210 A078693 A222421` `Adjacent sequences: A248096 A248097 A248098 * A248100 A248101 A248102`
	KEYWORD	`nonn`
	AUTHOR	`Emeric Deutsch, Jan 09 2015`
	STATUS	`approved`

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Last modified August 29 12:23 EDT 2024. Contains 375517 sequences. (Running on oeis4.)