A038091 Number of n-node rooted identity trees of height 7.

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

Links

Alois P. Heinz, Table of n, a(n) for n = 8..1000

Index entries for sequences related to rooted trees

Formula

A038086 - A038085.

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

Cf. A038081-A038093.

Column k=7 of A227819.

Sequence in context: A055909 A036596 A298408 * A027993 A028492 A059822

Adjacent sequences: A038088 A038089 A038090 * A038092 A038093 A038094

Keyword

nonn,fini

Author

Christian G. Bower, Jan 04 1999

Status

approved