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A144501
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Main diagonal of array in A144502.
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6
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1, 2, 30, 1633, 198773, 42965211, 14505751627, 7051160946740, 4664901181968498, 4030793305701978223, 4407914679125170417031, 5950921219972964057360847, 9721118017169914469460646225, 18898282608956442548700379478918, 43117198379072165094561711078882078, 114089724623922992953782697056886301761
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ 3^(3*n - 3/2) * n^(2*n - 1) / (2^(n-1) * exp(2*n - 1)). - Vaclav Kotesovec, Apr 06 2019
a(n) = ( 3*(3*n-4)*(3*n-8)*(9*n^2 - 21*n + 11)*a(n-1) + 3*(3*n-2)*a(n-2) - (3*n-5)*(3*n-2)*a(n-3) )/(2*(3*n-5)*(3*n-8)), with a(0) = 1, a(1) = 2, a(3) = 30. - G. C. Greubel, Oct 09 2023
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MATHEMATICA
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a[n_]:= a[n]= If[n==0, 1, If[n<3, 2*(15)^(n-1), (3*(3*n-4)*(3*n-8)*(9*n^2- 21*n+11)*a[n-1] +3*(3*n-2)*a[n-2] -(3*n-5)*(3*n-2)*a[n-3])/(2*(3*n-5)*(3*n-8))]];
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PROG
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(Magma) I:=[1, 2, 30]; [n le 3 select I[n] else ( 3*(3*n-7)*(3*n-11)*(9*n^2 - 39*n + 41)*Self(n-1) + 3*(3*n-5)*Self(n-2) - (3*n-8)*(3*n-5)*Self(n-3) )/(2*(3*n-8)*(3*n-11)): n in [1..30]]; // G. C. Greubel, Oct 09 2023
(SageMath)
@CachedFunction
if (n<3): return (1, 2, 30)[n]
else: return ( 3*(3*n-4)*(3*n-8)*(9*n^2 - 21*n + 11)*a(n-1) + 3*(3*n-2)*a(n-2) - (3*n-5)*(3*n-2)*a(n-3) )/(2*(3*n-5)*(3*n-8))
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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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