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A115277 Number of partitions of {1,...,n} into blocks such that no even sized block is repeated. 4
1, 1, 2, 5, 12, 37, 143, 562, 2320, 10941, 54865, 283890, 1604155, 9558226, 58668223, 384572975, 2631778832, 18576630237, 137919691717, 1060303298138, 8415786131309, 69538205444478, 591734670548037, 5194542789203877, 47127033586211659, 438972204436025198 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

FORMULA

E.g.f.: exp(sinh(x)) * Product {m >= 1} (1+x^(2*m)/(2*m)!).

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-1), j=0..min(

       `if`(irem(i, 2)=0, 1, n), n/i))))

    end:

a:= n-> b(n$2):

seq(a(n), n=0..30);  # 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-1], {j, 0, Min[If[Mod[i, 2]==0, 1, n], n/i]}]]]; a[n_] :=  b[n, n]; Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Oct 25 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A001935, A115275, A115276, A115278.

Sequence in context: A024717 A003724 A138314 * A130221 A036782 A050237

Adjacent sequences:  A115274 A115275 A115276 * A115278 A115279 A115280

KEYWORD

nonn

AUTHOR

Christian G. Bower, Jan 18 2006

STATUS

approved

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Last modified January 24 04:35 EST 2020. Contains 331183 sequences. (Running on oeis4.)