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A304914 Number of trees with positive integer edge labels summing to n. 2
1, 1, 2, 4, 9, 21, 55, 146, 415, 1212, 3653, 11246, 35346, 112750, 364714, 1193202, 3943557, 13148575, 44186841, 149536376, 509270554, 1744342614, 6005869285, 20777091355, 72192026878, 251848377631, 881865312582, 3098564357293, 10922162622233, 38614641384893 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..500

FORMULA

G.f.: g(x) + (g(x^2) - g(x)^2)*x/(2*(1-x)) where g(x) is the g.f. of A052855.

MATHEMATICA

max = 30; g[_] = 1; Do[g[x_] = Exp[Sum[(g[x^k]/(1 - x^k))*(x^k/k) + O[x]^n, {k, 1, n}]] // Normal, {n, 1, max}]; CoefficientList[g[x] + (g[x^2] - g[x]^2)*(x/(2*(1 - x))) + O[x]^max, x] (* Jean-François Alcover, May 25 2018 *)

PROG

(PARI) \\ here b(n) is A052855 as series

EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}

b(n)={my(v=[1]); for(i=2, n, v=concat([1], v + EulerT(v))); Ser(v)*(1-x)}

seq(n)={my(g=b(n)); Vec(g + (subst(g, x, x^2) - g^2)*x/(2*(1-x)))}

CROSSREFS

Row sums of A303842.

Cf. A052855.

Sequence in context: A106219 A198304 A032129 * A005217 A148072 A001430

Adjacent sequences:  A304911 A304912 A304913 * A304915 A304916 A304917

KEYWORD

nonn

AUTHOR

Andrew Howroyd, May 20 2018

STATUS

approved

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Last modified December 6 16:37 EST 2021. Contains 349567 sequences. (Running on oeis4.)