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A119551
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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.
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1
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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; internal format)
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OFFSET
| 1,9
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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!.
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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 (martin_n_fuller(AT)btinternet.com), Jun 26 2006
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CROSSREFS
| Cf. A076822 without restriction on product. A120690 without restriction on sum.
Sequence in context: A083774 A081518 A135616 * A100634 A130865 A105725
Adjacent sequences: A119548 A119549 A119550 * A119552 A119553 A119554
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KEYWORD
| nonn,nice
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AUTHOR
| Jens Voss (jens(AT)voss-ahrensburg.de), May 30 2006
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EXTENSIONS
| a(18) and a(19) from John W. Layman (layman(AT)math.vt.edu), Jun 08 2006
More terms from Martin Fuller (martin_n_fuller(AT)btinternet.com), Jun 26 2006
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