A145455 Exponential transform of C(n,5) = A000389.

1, 0, 0, 0, 0, 1, 6, 21, 56, 126, 378, 3234, 34056, 289575, 2020018, 12237225, 70634928, 468041756, 4190274648, 45557515620, 499503011496, 5121432107757, 49183015347774, 462331794763069, 4579813478536296, 50959878972009546

Offset: 0

Author

Alois P. Heinz, Oct 10 2008

Keywords

• nonn

Comments

a(n) is the number of ways of placing n labeled balls into indistinguishable boxes, where in each filled box 5 balls are seen at the top.

a(n) is also the number of forests of labeled rooted trees of height at most 1, with n labels, where each root contains 5 labels.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500
• N. J. A. Sloane, Transforms
• Index entries for sequences related to rooted trees

Crossrefs

5th column of A145460, A143398.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      add(binomial(n-1, j-1) *binomial(j,5) *a(n-j), j=1..n))
    end:
seq(a(n), n=0..30);

Mathematica

With[{nmax = 50}, CoefficientList[Series[Exp[Exp[x]*x^5/5!], {x, 0, nmax}], x]] (* G. C. Greubel, Nov 21 2017 *)

PARI

x='x+O('x^30); Vec(serlaplace(exp(exp(x)*x^5/5!))) \\ G. C. Greubel, Nov 21 2017

Formula

E.g.f.: exp(exp(x)*x^5/5!).