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A350267
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a(n) = n*hypergeom([1, 1 - n, -n], [2], 1) if n >= 1, a(0) = 1.
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2
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1, 1, 4, 18, 100, 675, 5376, 49294, 510728, 5894109, 74915740, 1039180186, 15613569324, 252501251743, 4371586879128, 80652138666870, 1579212732426256, 32701859350855769, 713914404925713588, 16384896394304282722, 394340620941231415540, 9929838681717090607611
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = n*A247499(n - 1) for n >= 1.
a(n) = Sum_{k=1..n} binomial(n, k)^2 * k! / (n - k + 1), for n >= 1.
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MAPLE
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A350267 := n -> ifelse(n = 0, 1, n)*hypergeom([1, 1 - n, -n], [2], 1):
seq(simplify(A350267(n)), n = 0..21);
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MATHEMATICA
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a[0] = 1; a[n_] := Sum[Binomial[n, k]^2 * k!/(n - k + 1), {k, 1, n}]; Array[a, 20, 0] (* Amiram Eldar, Jan 09 2022 *)
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PROG
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(PARI) a(n) = if (n == 0, 1, sum(k=1, n, binomial(n, k)^2 * k! / (n - k + 1))); \\ Michel Marcus, Jan 09 2022 [a(0) corrected by Georg Fischer, Jun 22 2022]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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