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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A032310 Number of ways to partition n labeled elements into sets of odd sizes, with all sizes different. 5
 1, 1, 0, 1, 4, 1, 6, 1, 64, 505, 130, 1321, 1024, 13157, 2380, 395851, 5782144, 1639617, 24545706, 16100905, 306621184, 292018525, 6304002100, 1549052715, 507969498304, 11794047630801, 3164830777316, 75389026652551, 48756350408224, 1240389053007865 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..500 C. G. Bower, Transforms (2) FORMULA "EGJ" (unordered, element, labeled) transform of 1, 0, 1, 0... (odds) E.g.f.: Product_{k>0} (1+x^(2*k-1)/(2*k-1)!). - Vladeta Jovovic, Jan 16 2004 MAPLE with(combinat): b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add( multinomial(n, n-i*j, i\$j)/j!*b(n-i*j, i-2), j=0..min(1, n/i)))) end: a:= n-> b(n, iquo(n+1, 2)*2-1): seq(a(n), n=0..40); # Alois P. Heinz, Mar 08 2015 MATHEMATICA multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Sum[multinomial[n, Join[{n-i*j}, Array[i&, j]]]/j!*b[n - i*j, i-2], {j, 0, Min[1, n/i]}]]]; a[n_] := b[n, Quotient[n+1, 2]*2-1]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 05 2017, after Alois P. Heinz *) CROSSREFS Cf. A003724. Sequence in context: A316223 A087652 A072195 * A032220 A032145 A032050 Adjacent sequences: A032307 A032308 A032309 * A032311 A032312 A032313 KEYWORD nonn AUTHOR EXTENSIONS Description corrected by Vladeta Jovovic, Aug 18 2004 a(0)=1 prepended by Alois P. Heinz, Mar 08 2015 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 February 5 20:57 EST 2023. Contains 360087 sequences. (Running on oeis4.)