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A099021
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Main diagonal of array in A099020.
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2
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1, 1, 4, 24, 198, 2070, 26160, 387240, 6565020, 125341020, 2659925520, 62089917120, 1580632348680, 43571319671880, 1292731109429760, 41068078953501600, 1390717740470058000, 50003952605673066000, 1902359109096675028800, 76341746199227491382400
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OFFSET
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0,3
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COMMENTS
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Diagonal of Euler-Seidel matrix with start sequence A001147.
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LINKS
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FORMULA
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a(n) = (1/(sqrt(2*Pi)))*Int(exp(-x^2/2)*(x(1+x))^n,x,-infinity,infinity). - Paul Barry, Apr 19 2010
E.g.f.: exp(x^2/(2-4*x))/sqrt(1-2*x).
Recurrence: a(n) = (4*n-3)*a(n-1) - (n-1)*(4*n-7)*a(n-2) - (n-2)*(n-1)*a(n-3).
a(n) ~ 2^(n-1/2)*exp(sqrt(n/2)-n-3/16)*n^n.
(End)
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MAPLE
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a:= proc(n) a(n):= `if`(n<3, [1, 1, 4][n+1],
(4*n-3)*a(n-1) -(n-1)*(4*n-7)*a(n-2) -(n-2)*(n-1)*a(n-3))
end:
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MATHEMATICA
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Table[n!*SeriesCoefficient[E^(x^2/(2-4*x))/Sqrt[1-2*x], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 14 2012 *)
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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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