A304914 Number of trees with positive integer edge labels summing to n.

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

Offset: 0

Author

Andrew Howroyd, May 20 2018

Keywords

• nonn

Links

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

Crossrefs

Row sums of A303842.

Cf. A052855.

Programs

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 *)

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)))}

Formula

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