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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 (list; graph; refs; listen; history; text; internal format)
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<=0||m<=1||s<=c||s>m*c, c==s&&p==1, x=valuation(p, m); sum(i=x*isprime(m), x, b(c-i, s-m*i, p/m^i, m-1)))); 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

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Last modified November 14 10:04 EST 2019. Contains 329111 sequences. (Running on oeis4.)