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 A002569 Max_{k=0..n} { Number of partitions of n into exactly k parts }. (Formerly M0283 N0101) 7
 1, 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 11, 15, 18, 23, 30, 37, 47, 58, 71, 90, 110, 136, 164, 201, 248, 300, 364, 436, 525, 638, 764, 919, 1090, 1297, 1549, 1845, 2194, 2592, 3060, 3590, 4242, 5013, 5888, 6912, 8070, 9418, 11004, 12866, 15021, 17475, 20298, 23501, 27169 (list; graph; refs; listen; history; text; internal format)
 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, Table of n, a(n) for n = 0..3000 (n = 0..97 from Robert G. Wilson v) 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] 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 Cf. A000041, A008284, A026819, A046155. Sequence in context: A122130 A003073 A123946 * A129528 A280200 A052336 Adjacent sequences:  A002566 A002567 A002568 * A002570 A002571 A002572 KEYWORD nonn AUTHOR EXTENSIONS More terms from David W. Wilson STATUS approved

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Last modified August 18 08:57 EDT 2019. Contains 326077 sequences. (Running on oeis4.)