OFFSET
1,3
COMMENTS
For n > 2, a(n) is also the number of partitions of n into parts <= n-2: a(n) = A026820(n+1, n-1). - Reinhard Zumkeller, Jan 21 2010
Also, the number of partitions of 2*n in which n-1 is the maximal part; see the Mathematica section. - Clark Kimberling, Mar 13 2012
This is column 2 of the matrix A in Sect. 2.3 of the Govindarajan preprint, cf. references and A096651. - M. F. Hasler, Apr 12 2012
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
S. Govindarajan, Notes on higher-dimensional partitions, arXiv:1203.4419 [math.CO], 2012.
R. K. Guy, Letter to N. J. A. Sloane, Aug. 1992.
R. K. Guy, Parker's permutation problem involves the Catalan numbers, Preprint, 1992. (Annotated scanned copy)
R. K. Guy, Parker's permutation problem involves the Catalan numbers, Amer. Math. Monthly 100 (1993), 287-289.
FORMULA
a(n) = A000041(n+1) - 2. - Vladeta Jovovic, Oct 06 2001
MATHEMATICA
f[n_]:= Length[Select[IntegerPartitions[2 n], First[#]==n-1 &]]; Table[f[n], {n, 1, 24}] (* Clark Kimberling, Mar 13 2012 *)
a[n_]:= PartitionsP[n+1]-2; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Jan 28 2015, after M. F. Hasler *)
PROG
(PARI) A007042(n)=numbpart(n+1)-2 \\ M. F. Hasler, Apr 12 2012
(Julia)
using Nemo
function A007042List(len)
R, z = PolynomialRing(ZZ, "z")
e = eta_qexp(-1, len+2, z)
[coeff(e, j) - 2 for j in 2:len+1] end
A007042List(45) |> println # Peter Luschny, May 30 2020
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from James A. Sellers
Name edited by Petros Hadjicostas, May 31 2020
STATUS
approved