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A032310 Number of ways to partition n labeled elements into sets of odd sizes, with all sizes different. 3
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-Fran├žois 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

Christian G. Bower

EXTENSIONS

Description corrected by Vladeta Jovovic, Aug 18 2004

a(0)=1 prepended by Alois P. Heinz, Mar 08 2015

STATUS

approved

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Last modified October 18 07:00 EDT 2018. Contains 316307 sequences. (Running on oeis4.)