OFFSET
1,5
COMMENTS
(1, 1, 2, 3, 5, 8, ...) convolved with (0, 0, 1, 2, 4, 7, ...) = (0, 0, 1, 3, 8, ...). - Gary W. Adamson, Aug 14 2010
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
N. J. A. Sloane, Table of n, a(n) for n=1..200
J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.
J. Riordan, The enumeration of trees by height and diameter, IBM Journal 4 (1960), 473-478. (Annotated scanned copy)
N. J. A. Sloane, Maple programs for counting rooted trees by height (after Riordan)
FORMULA
MAPLE
# For Maple program see link.
with(combstruct):
ZL:= proc(m) local i; [T0, {seq(T||i=Prod(Z, Set(T||(i+1))), i=0..m-1), T||m=Z}, unlabeled] end: A000235:= n-> count(ZL(3), size=n)-count(ZL(2), size=n): seq(A000235(n), n=1..36); # Zerinvary Lajos, Sep 23 2007
MATHEMATICA
m = 36; Rest @ CoefficientList[ Series[x*Product[(1-x^k)^(-PartitionsP[k-1]), {k, 1, m}], {x, 0, m}], x] - PartitionsP[Range[0, m-1]] (* Jean-François Alcover, Jul 05 2011, after Christian G. Bower *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved