The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A309999 Number of distinct values of multinomial coefficients M(n;lambda) where lambda ranges over all partitions of n into distinct parts. 3
 1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 25, 32, 35, 44, 53, 61, 72, 81, 98, 114, 130, 147, 176, 200, 229, 257, 291, 342, 387, 442, 501, 573, 642, 714, 807, 907, 1037, 1159, 1293, 1458, 1624, 1811, 2024, 2246, 2505, 2785, 3114, 3449, 3795, 4213, 4660 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Differs from A000009 first at n = 15: a(15) = 25 < 27 = A000009(15). There are two repeated multinomial coefficients for n = 15: 1365 = M(15;11,4) = M(15;12,2,1) and 30030 = M(15;9,5,1) = M(15;10,3,2). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..125 Wikipedia, Multinomial coefficients Wikipedia, Partition (number theory) MAPLE g:= proc(n, i) option remember; `if`(i*(i+1)/2binomial(n, i)*x, g(n-i, min(n-i, i-1)))[], g(n, i-1)[]})) end: a:= n-> nops(g(n\$2)): seq(a(n), n=0..55); MATHEMATICA g[n_, i_] := g[n, i] = If[i(i+1)/2 < n, {}, If[n == 0, {1}, Union[ Binomial[n, i] #& /@ g[n - i, Min[n - i, i - 1]], g[n, i - 1]]]]; a[n_] := Length[g[n, n]]; a /@ Range[0, 55] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *) CROSSREFS Cf. A000009, A070289. Sequence in context: A027581 A058706 A034143 * A034144 A347586 A287997 Adjacent sequences: A309996 A309997 A309998 * A310000 A310001 A310002 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 26 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 3 03:45 EDT 2023. Contains 363103 sequences. (Running on oeis4.)