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A038085 Number of n-node rooted identity trees of height at most 6. 5
1, 1, 1, 2, 3, 6, 12, 24, 45, 85, 157, 289, 529, 969, 1764, 3208, 5807, 10493, 18901, 33977, 60919, 109019, 194662, 346940, 617148, 1095884, 1942576, 3437834, 6074239, 10716076, 18877025, 33205498, 58328831, 102323302, 179267087, 313674445, 548183968 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The number of terms is A038093(6), a number that is too large to write down!

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 A038084 and shift right.

MAPLE

weigh:= proc(p) proc(n) `if`(n<0, 1, coeff(mul((1+x^k)^p(k), k=1..n), x, n)) end end: wsh:= p-> n-> weigh(p)(n-1): a:= (wsh@@3)(n-> `if`(n>0 and n<12, [1$3, 2$5, 1$3][n], 0)): seq(a(n), n=1..40);  # Alois P. Heinz, Sep 10 2008

MATHEMATICA

Nest[CoefficientList[Series[Product[(1+x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 36}], x]&, {1}, 6] (* Geoffrey Critzer, Aug 01 2013 *)

CROSSREFS

Cf. A038081-A038093.

Sequence in context: A029996 A294123 A321048 * A124313 A049890 A262236

Adjacent sequences:  A038082 A038083 A038084 * A038086 A038087 A038088

KEYWORD

nonn,fini

AUTHOR

Christian G. Bower, Jan 04 1999

STATUS

approved

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Last modified February 16 15:17 EST 2020. Contains 331961 sequences. (Running on oeis4.)