OFFSET
0,2
COMMENTS
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000 (first 250 terms from Reinhard Zumkeller)
FORMULA
G.f.: 1/((1-x)*Product_{j>=2} (1 - x^(j!/2))).
EXAMPLE
a(3) = 5 because the partitions of 6 into factorials are [6], [2,2,2], [2,2,1,1], [2,1,1,1,1] and [1,1,1,1,1,1].
MAPLE
g:=1/(1-x)/product(1-x^(j!/2), j=2..7): gser:=series(g, x=0, 70): seq(coeff(gser, x, n), n=0..65);
# second Maple program
b:= proc(n, i) option remember;
`if`(n=0 or i=1, 1, b(n, i-1)+
`if`(i!>n, 0, b(n-i!, i)))
end:
a:= proc(n) local i;
for i while(i!<2*n) do od;
b(2*n, i)
end:
seq(a(n), n=0..100); # Alois P. Heinz, Jun 13 2012
MATHEMATICA
f[n_] := Length@ IntegerPartitions[2 n, All, {1, 2, 6, 24, 120}]; Array[f, 57, 0] (* Robert G. Wilson v, Oct 02 2014 *)
b[n_, i_] := b[n, i] = If[n==0 || i==1, 1, b[n, i-1] + If[i!>n, 0, b[n-i!, i] ] ]; a[n_] := Module[{i}, For[i=1, i!<2*n, i++]; b[2*n, i]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jun 29 2015, after Alois P. Heinz *)
PROG
(Haskell)
a117930 n = p (tail a000142_list) $ 2*n where
p _ 0 = 1
p ks'@(k:ks) m | m < k = 0
| otherwise = p ks' (m - k) + p ks m
-- Reinhard Zumkeller, Dec 04 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Apr 04 2006
EXTENSIONS
An incorrect g.f. was deleted by N. J. A. Sloane, Sep 16 2009
STATUS
approved