A394498 Number of ordered rooted trees with total edge weight n such that all groups of sibling edges have weights in standard order.

1, 1, 2, 6, 19, 64, 226, 823, 3069, 11662, 44994, 175786, 694046, 2764948, 11100479, 44866104, 182415539, 745552212, 3061404801, 12623552262, 52249572370, 217005775517, 904096373006, 3777439157760, 15824068559803, 66448827174668, 279656985998353, 1179403960819100

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Formula

G.f.: A(x) satisfies A(x) = Sum_{j>=0} x^(j*(j+1)/2) * A(x)^j / Product_{k=1..j} (1 - A(x) * (x - x^(k+1))/(1-x)).

Prog

(PARI)
tri(n) = {n*(n+1)/2}
A_x(N) = {my(x='x+O('x^(N+1)), A=1); for(i=1, N, A = sum(j=0, N, (x^tri(j) * A^j)/prod(k=1, j, (1 - A * (x - x^(k+1))/(1-x))  ))); Vec(A)}

Crossrefs

Row sums of A395304.

Cf. A383253.

Sequence in context: A119370 A192738 A192728 * A181315 A181734 A216447

Adjacent sequences: A394495 A394496 A394497 * A394499 A394500 A394502

Keyword

nonn

Author

John Tyler Rascoe, Apr 19 2026

Status

approved