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A036722 G.f. satisfies A(x) = 1 + x*cycle_index(Sym(6), A(x)). 12
1, 1, 1, 2, 4, 9, 20, 48, 114, 283, 710, 1816, 4690, 12267, 32338, 85978, 230080, 619521, 1676808, 4560286, 12454272, 34143682, 93928091, 259208006, 717375068, 1990625390, 5537142610, 15436744525, 43124847431, 120708508008, 338477040445, 950714584576 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(n) is also the number of rooted trees where each node has at most 6 children. [Patrick Devlin, Apr 29 2012]

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = Sum_{j=1..6} A244372(n,j) for n>0, a(0) = 1. - Alois P. Heinz, Sep 19 2017

MAPLE

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

      `if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*

       b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))

    end:

a:= n-> `if`(n=0, 1, b(n-1$2, 6$2)):

seq(a(n), n=0..35);  # Alois P. Heinz, Sep 20 2017

CROSSREFS

Cf. A000081, A036717, A036718, A036719, A036720, A036721, A182378, A244372, A292553, A292554, A292555, A292556.

Column k=6 of A299038.

Sequence in context: A036625 A003019 A036626 * A255637 A215796 A034824

Adjacent sequences:  A036719 A036720 A036721 * A036723 A036724 A036725

KEYWORD

nonn,changed

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 23 00:33 EST 2018. Contains 299473 sequences. (Running on oeis4.)