

A119551


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! and whose sum is n * (n + 1) / 2.


1



1, 1, 1, 1, 1, 1, 1, 1, 2, 6, 6, 22, 22, 60, 159, 377, 377, 1007, 1007, 2867, 8147, 22403, 22403, 67808, 176128, 495053, 1362240, 4210266, 4210266, 14223808, 14223808, 42235255, 129279396, 370630653, 1178215490
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OFFSET

1,9


LINKS

Table of n, a(n) for n=1..35.


EXAMPLE

a(9) = 2 because the sequences (1, 2, 3, 4, 5, 6, 7, 8, 9) and (1, 2, 4, 4, 4, 5, 7, 9, 9) both add up to 45 and multiply up to 9!.


PROG

(PARI) a(n) = (b(c, s, p, m) = local(x); if(c<=0m<=1s<=cs>m*c, c==s&&p==1, x=valuation(p, m); sum(i=x*isprime(m), x, b(ci, sm*i, p/m^i, m1)))); b(n, n*(n+1)/2, n!, n)  Martin Fuller, Jun 26 2006


CROSSREFS

Cf. A076822 without restriction on product. A120690 without restriction on sum.
Sequence in context: A081518 A258702 A320916 * A100634 A242527 A304680
Adjacent sequences: A119548 A119549 A119550 * A119552 A119553 A119554


KEYWORD

nonn,nice


AUTHOR

Jens Voß, May 30 2006


EXTENSIONS

a(18) and a(19) from John W. Layman, Jun 08 2006
More terms from Martin Fuller, Jun 26 2006


STATUS

approved



