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A038083
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Number of n-node rooted identity trees of height at most 4.
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5
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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
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OFFSET
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1,4
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COMMENTS
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A finite sequence with A038093(4) = 97 terms.
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LINKS
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FORMULA
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Take Weigh transform of A038082 and shift right.
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MAPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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