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A130220 Number of partitions of n-set in which number of blocks of size k is odd (or zero) for every k. 5
1, 1, 1, 5, 5, 27, 117, 331, 1213, 6579, 47193, 140527, 1213841, 4617927, 48210879, 243443739, 2392565149, 10377087115, 125434781845, 725455816883, 8086277450629, 59694530600595, 614469256831895, 4650128350629285 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
E.g.f.: Product_{k>0} (1+sinh(x^k/k!)).
EXAMPLE
a(4)=5 because we have abcd, a|bcd, acd|b, abd|c and abc|d.
MAPLE
g:=product(1+sinh(x^k/factorial(k)), k=1..30): gser:=series(g, x=0, 28): seq(factorial(n)*coeff(gser, x, n), n=0..24); # Emeric Deutsch, Sep 01 2007
# second Maple program:
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(`if`(j=0 or irem(j, 2)=1, multinomial(n, n-i*j, i$j)
/j!*b(n-i*j, i-1), 0), j=0..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[If[j == 0 || Mod[j, 2] == 1, multinomial[n, Join[{n - i*j}, Array[i&, j]]]/j!*b[n-i*j, i-1], 0], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Nov 11 2015, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A220078 A302000 A219351 * A081847 A203124 A305180
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Aug 04 2007, Aug 05 2007
EXTENSIONS
More terms from Emeric Deutsch, Sep 01 2007
STATUS
approved

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Last modified February 29 23:21 EST 2024. Contains 370428 sequences. (Running on oeis4.)