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A120690 Number of ordered finite sequences a_1 <= a_2 <= ... <= a_n of length n of positive integers less than or equal to n whose product is n!. 1
1, 1, 1, 1, 2, 2, 6, 6, 13, 33, 97, 97, 306, 306, 896, 2804, 7974, 7974, 24929, 24929, 82612, 263913, 782310, 782310, 2692708, 7705973, 22901921, 69066986, 232517327, 232517327, 853599455, 853599455, 2737549933, 8929178758, 26621287019, 90741181490, 325528535021, 325528535021 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
FORMULA
a(p) = a(p-1) for prime p. - Alois P. Heinz, Jul 05 2022
EXAMPLE
a(5) = 2 because 5! = 1*2*3*4*5 = 2*2*2*3*5.
MATHEMATICA
a[n_] := a[n] = Module[{b}, b[c_, p_, m_] := b[c, p, m] = Module[{x}, If[c <= 0 || m <= 1 || p > m^c, Boole[p == 1], x = IntegerExponent[p, m]; Sum[b[c - i, p/m^i, m - 1], {i, x*Boole@PrimeQ[m], x}]]]; b[n, n!, n]];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 37}] (* Jean-François Alcover, Jul 05 2022, after Martin Fuller *)
PROG
(PARI) a(n) = (b(c, p, m) = local(x); if(c<=0||m<=1||p>m^c, p==1, x=valuation(p, m); sum(i=x*isprime(m), x, b(c-i, p/m^i, m-1)))); b(n, n!, n)
CROSSREFS
Sequence in context: A337735 A060549 A228315 * A165124 A288302 A286409
KEYWORD
nonn
AUTHOR
Martin Fuller, Jun 26 2006
EXTENSIONS
a(0)=1 prepended and a(24)-a(37) added by Alois P. Heinz, Jul 05 2022
STATUS
approved

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Last modified March 29 08:53 EDT 2024. Contains 371268 sequences. (Running on oeis4.)