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A158887
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a(n) = (n+1)^n * n! * C(n-1 + 1/(n+1), n).
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1
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1, 1, 4, 45, 1056, 43225, 2756160, 253586025, 31872332800, 5252921480961, 1099886703552000, 285322741626047125, 89844523369696972800, 33764841634845724313625, 14930493174337400252809216
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n) = Product_{k=0..n-1} (k*(n+1) + 1) for n>0 with a(0)=1.
a(n) = coefficient of x^n/(n!*(n+1)^n) in 1/(1-x)^(1/(n+1)).
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EXAMPLE
| a(1) = 1, a(2) = 1*4, a(3) = 1*5*9, a(4) = 1*6*11*16, a(5) = 1*7*13*19*25.
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MATHEMATICA
| Table[(n+1)^n n!Binomial[n-1+1/(n+1), n], {n, 0, 20}] (* From Harvey P. Dale, Oct 26 2011 *)
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PROG
| (PARI) a(n)=(n+1)^n*n!*polcoeff(1/(1-x+x*O(x^n))^(1/(n+1)), n)
(PARI) a(n)=if(n==0, 1, prod(k=0, n-1, k*(n+1)+1))
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CROSSREFS
| Sequence in context: A107668 A197989 A174484 * A126452 A082765 A132873
Adjacent sequences: A158884 A158885 A158886 * A158888 A158889 A158890
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), May 01 2009
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