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A236696 Number of forests on n vertices consisting of labeled rooted trees of the same size. 9
1, 3, 10, 77, 626, 8707, 117650, 2242193, 43250842, 1049248991, 25937424602, 772559330281, 23298085122482, 817466439388341, 29223801257127976, 1181267018656911617, 48661191875666868482, 2232302772999145783735, 104127350297911241532842 (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(d divides n, n!/(n/d)!*(d^(d-1)/d!)^(n/d) ).

E.g.f.: sum(k>=1, exp(k^(k-1)*x^k/k!)).

EXAMPLE

For n = 3 we have the following 10 forests (where the roots are denoted by ^):

                              3  2  3  1  2  1

                              |  |  |  |  |  |

         2   3  1   3  1   2  2  3  1  3  1  2

          \ /    \ /    \ /   |  |  |  |  |  |

  1 2 3    1      2      3    1  1  2  2  3  3

  ^ ^ ^,   ^,     ^,     ^,   ^, ^, ^, ^, ^, ^

MATHEMATICA

Table[Sum[n!/(n/d)!*(d^(d-1)/d!)^(n/d), {d, Divisors[n]}], {n, 1, 100}]

PROG

(Maxima) a(n):= lsum(n!/(n/d)!*(d^(d-1)/d!)^(n/d), d, listify(divisors(n))); makelist(a(n), n, 1, 40); /* Emanuele Munarini, Feb 03 2014 */

CROSSREFS

Cf. A000169, A038041, A005225, A055225.

Sequence in context: A082245 A158033 A027159 * A262259 A203492 A320258

Adjacent sequences:  A236693 A236694 A236695 * A236697 A236698 A236699

KEYWORD

nonn

AUTHOR

Emanuele Munarini, Jan 30 2014

STATUS

approved

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Last modified December 13 12:37 EST 2019. Contains 329968 sequences. (Running on oeis4.)