OFFSET
0,5
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
Robert Israel and Robert G. Wilson v, Table of n, a(n) for n = 0..3000 (n = 0..97 from Wilson)
F. C. Auluck, S. Chowla and H. Gupta, On the maximum value of the number of partitions into k parts, J. Indian Math. Soc., 6 (1942), 105-112. [Annotated scanned copy. But the last page is in a separate file: see the next link.]
F. C. Auluck, S. Chowla and H. Gupta, On the maximum value of the number of partitions into k parts, [Annotated scanned copy of page 112 only]
Victor Meally, Comparison of several sequences given in Motzkin's paper "Sorting numbers for cylinders...", letter to N. J. A. Sloane, N. D.
T. S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176 (p. 172, gives a(9) incorrectly as 6). [Annotated, scanned copy]
OEIS Wiki, Sorting numbers
MAPLE
1, seq(max(seq(combinat:-numbpart(n, k)-combinat:-numbpart(n, k-1), k=1..n)), n=1..100); # Robert Israel, Nov 24 2014
MATHEMATICA
f[n_] := Block[{k = 1, mx = 0}, While[k < n + 1, a = Length@ IntegerPartitions[n, {k}]; If[a > mx, mx = a]; k++ ]; mx]; Array[f, 53] (* Robert G. Wilson v, Jul 20 2010 *)
t[0, k_] := 1; t[1, k_] := 1 /; k > 0; t[n_, k_] := 0 /; n < 0; t[n_, 0] := 0 /; n > 0; t[n_, 1] := 1 /; n > 0; t[n_, k_] := t[n, k] = Sum[t[n - k + i, k - i], {i, 0, k - 1}];
f[n_] := Max[ Table[ t[n - k, k], {k, 0, n}]]; Array[f, 54, 0] (* Robert G. Wilson v, Nov 24 2014 *)
Max[CoefficientList[#, a]] & /@ (1/QPochhammer[a q, q] + O[q]^60)[[3]] (* Vladimir Reshetnikov, Nov 17 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from David W. Wilson
STATUS
proposed