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A038087 Number of n-node rooted identity trees of height at most 8. 3
1, 1, 1, 2, 3, 6, 12, 25, 52, 112, 238, 503, 1053, 2194, 4547, 9406, 19401, 39965, 82189, 168837, 346380, 709917, 1453380, 2972636, 6074138, 12400794, 25295272, 51556337, 104998985, 213681811, 434548933, 883104930, 1793484049, 3640032699, 7383188993 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A finite sequence with a very large number of terms, A038093(8). The sum of all terms is 2^(2^(2^(2^65536))).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

N. J. A. Sloane, Transforms

Index entries for sequences related to rooted trees

FORMULA

Take Weigh transform of A038086 and shift right.

MAPLE

weigh:= proc(p) proc(n) local x, k; coeff(series(mul((1+x^k)^p(k), k=1..n), x, n+1), x, n) end end: wsh:= p-> n-> weigh(p)(n-1): a:= (wsh@@5)(n-> `if`(n>0 and n<12, [1$3, 2$5, 1$3][n], 0)): seq(a(n), n=1..33);  # Alois P. Heinz, Sep 10 2008

MATHEMATICA

Nest[CoefficientList[Series[Product[(1+x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 36}], x]&, {1}, 8] (* Geoffrey Critzer, Aug 01 2013 *)

CROSSREFS

Cf. A038081-A038093.

Sequence in context: A032305 A032218 A005829 * A116379 A116380 A004111

Adjacent sequences:  A038084 A038085 A038086 * A038088 A038089 A038090

KEYWORD

nonn,fini

AUTHOR

Christian G. Bower, Jan 04 1999

STATUS

approved

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Last modified October 20 17:39 EDT 2017. Contains 293648 sequences.