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A038086 Number of n-node rooted identity trees of height at most 7. 5
1, 1, 1, 2, 3, 6, 12, 25, 51, 105, 211, 421, 832, 1641, 3224, 6328, 12382, 24200, 47197, 91915, 178683, 346897, 672443, 1301850, 2517078, 4860938, 9376300, 18066270, 34772627, 66859667, 128427832, 246456677, 472519632, 905131358, 1732313955, 3312661001 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The number of terms is A038093(7), 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 A038085 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@@4)(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}, 7] (* Geoffrey Critzer, Aug 01 2013 *)

CROSSREFS

Cf. A038081-A038093.

Sequence in context: A187741 A216632 A077903 * A032305 A032218 A005829

Adjacent sequences:  A038083 A038084 A038085 * A038087 A038088 A038089

KEYWORD

nonn,fini

AUTHOR

Christian G. Bower, Jan 04 1999

STATUS

approved

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Last modified February 26 11:49 EST 2020. Contains 332279 sequences. (Running on oeis4.)