STATUS
reviewed
approved
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Revision History for A102760
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Number of partitions of n-set into "lists", in which every even list appears an even number of times, cf. A000262.
(history; published version)
(history; published version)
STATUS
proposed
reviewed
STATUS
editing
proposed
MATHEMATICA
multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Sum[If[EvenQ[i] && OddQ[j], 0, b[n-i*j, i- 1] * multinomial[n, Join[{n - i*j}, Array[i &, j]]]/j!*i!^j], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 05 2017, after Alois P. Heinz *)
STATUS
approved
editing
STATUS
editing
approved
STATUS
editing
approved
LINKS
Alois P. Heinz, <a href="/A102760/b102760.txt">Table of n, a(n) for n = 0..445</a>
MAPLE
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(`if`(i::even and j::odd, 0, b(n-i*j, i-1)*
multinomial(n, n-i*j, i$j)/j!*i!^j), j=0..n/i)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..25); # Alois P. Heinz, May 10 2016
DATA
1, 1, 1, 7, 37, 241, 1381, 13231, 140617, 1483777, 16211881, 217551511, 3384215341, 50221272817, 782154787597, 13913712591871, 272739557719441, 5282625708305281, 106588332600443857, 2354480141600267047, 56238135934525073461, 1338131691952924913521
OFFSET
1,3
0,4
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, May 10 2016
STATUS
approved
editing
AUTHOR
_Vladeta Jovovic (vladeta(AT)eunet.rs), _, Feb 10 2005