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A038083 Number of n-node rooted identity trees of height at most 4. 5
1, 1, 1, 2, 3, 5, 7, 10, 13, 18, 24, 32, 41, 52, 66, 83, 102, 124, 152, 181, 216, 255, 299, 346, 400, 458, 521, 588, 659, 735, 814, 896, 979, 1067, 1151, 1239, 1324, 1407, 1486, 1564, 1635, 1700, 1759, 1809, 1853, 1887, 1912, 1925, 1932, 1925, 1912, 1887, 1853 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A finite sequence with A038093(4) = 97 terms.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..97

N. J. A. Sloane, Transforms

Index entries for sequences related to rooted trees

FORMULA

Take Weigh transform of A038082 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(n-> `if`(n>0 and n<12, [1$3, 2$5, 1$3][n], 0)): seq(a(n), n=1..97); # Alois P. Heinz, Sep 10 2008

MATHEMATICA

a = Drop[CoefficientList[ Series[x (1 + x) (1 + x^2) (1 + x^3) (1 + x^4), {x, 0, 11}], x], 1]; nn = 97; Drop[ CoefficientList[ Series[x Product[(1 + x^i)^a[[i]], {i, 1, 11}], {x, 0, nn}], x], 1] (* Geoffrey Critzer, Aug 01 2013 *)

CROSSREFS

Cf. A038081-A038093.

Sequence in context: A118199 A239883 A088318 * A238863 A060688 A005691

Adjacent sequences:  A038080 A038081 A038082 * A038084 A038085 A038086

KEYWORD

nonn,fini,full

AUTHOR

Christian G. Bower, Jan 04 1999

STATUS

approved

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Last modified April 22 14:30 EDT 2019. Contains 322356 sequences. (Running on oeis4.)