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A038091
Number of n-node rooted identity trees of height 7.
3
1, 6, 20, 54, 132, 303, 672, 1460, 3120, 6575, 13707, 28296, 57938, 117764, 237878, 477781, 954910, 1899930, 3765054, 7433724, 14628436, 28698388, 56143591, 109550807, 213251179, 414190801, 802808056, 1553046868, 2998986556, 5781366468, 11127506290
OFFSET
8,2
COMMENTS
The number of terms with a(n)>0 is A038093(7) - 7. - Alois P. Heinz, Sep 22 2013
FORMULA
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): f:= n-> `if`(n>0 and n<12, [1$3, 2$5, 1$3][n], 0): a:= (wsh@@4)(f)-(wsh@@3)(f): seq(a(n), n=8..36); # Alois P. Heinz, Sep 10 2008
MATHEMATICA
f[n_]:=Nest[CoefficientList[Series[Product[(1+x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 50}], x]&, {1}, n]; Drop[f[7]-PadRight[f[6], Length[f[7]]], 7] (* Geoffrey Critzer, Aug 01 2013 *)
CROSSREFS
Column k=7 of A227819.
Sequence in context: A055909 A036596 A298408 * A027993 A028492 A059822
KEYWORD
nonn,fini
AUTHOR
Christian G. Bower, Jan 04 1999
STATUS
approved