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A326396 Total number of colors in all series-reduced rooted trees with n leaves where colors span an initial interval of the color palette. 3
1, 3, 26, 322, 5210, 104421, 2491498, 68907073, 2166242180, 76266794945, 2972079029674, 126987589678185, 5902427979920102, 296484317531254557, 16003975713659818226, 923838934059255332723, 56788871072327503930862, 3703444074072753204057172 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..200

FORMULA

a(n) = Sum_{k=1..n} k * A319376(n,k).

From Vaclav Kotesovec, Sep 18 2019: (Start)

a(n) ~ c * d^n * n^n, where d = 1.37392076830840090205551979... and c = 0.29889555940946459367729...

a(n) ~ n*A316651(n)/(2*log(2)). (End)

MAPLE

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,

      add(binomial(A(i, k)+j-1, j)*b(n-i*j, i-1, k), j=0..n/i)))

    end:

A:= (n, k)-> `if`(n<2, n*k, b(n, n-1, k)):

a:= n-> add(k*add(A(n, k-j)*(-1)^j*binomial(k, j), j=0..k-1), k=1..n):

seq(a(n), n=1..20);

CROSSREFS

Cf. A316651, A319376.

Sequence in context: A126738 A283298 A259610 * A109074 A227020 A119293

Adjacent sequences:  A326393 A326394 A326395 * A326397 A326398 A326399

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 11 2019

STATUS

approved

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Last modified March 29 03:09 EDT 2020. Contains 333104 sequences. (Running on oeis4.)