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A036246
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CONTINUANT transform of squares 1, 4, 9, ...
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8
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1, 5, 46, 741, 18571, 669297, 32814124, 2100773233, 170195445997, 17021645372933, 2059789285570890, 296626678767581093, 50131968501006775607, 9826162452876095600065, 2210936683865622516790232, 566009617232052240393899457, 163578990316746963096353733305
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OFFSET
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1,2
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COMMENTS
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Denominator of fraction equal to the continued fraction [ 0, 1, 4, ...n^2 ].
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..100
N. J. A. Sloane, Transforms
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FORMULA
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a(n) ~ c * n^(2*n + 1) / exp(2*n), where c = 8.1245591771139376779472290412302409841950717664641832772206241208918274428499... - Vaclav Kotesovec, Jun 05 2018
From Jianing Song, Nov 30 2019: (Start)
a(n) = n^2 * a(n-1) + a(n-2) for n > 2.
Lim_{n->oo} A036245(n)/a(n) = A073824. (End)
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MAPLE
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a:= proc(n) option remember; `if`(n<0, 0,
`if`(n=0, 1, n^2 *a(n-1) +a(n-2)))
end:
seq(a(n), n=1..20); # Alois P. Heinz, Aug 06 2013
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MATHEMATICA
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Table[Denominator[FromContinuedFraction[Range[0, n]^2]], {n, 20}] (* Harvey P. Dale, Jul 16 2017 *)
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PROG
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(PARI) A036246(n) = my(v=vector(n+1)); for(i=1, n+1, if(i==1, v[i]=1, if(i==2, v[i]=1, v[i]=(i-1)^2*v[i-1]+v[i-2]))); v[n+1] \\ Jianing Song, Nov 30 2019
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CROSSREFS
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Cf. A036245, A073824.
Sequence in context: A339229 A295552 A066998 * A183240 A299715 A000872
Adjacent sequences: A036243 A036244 A036245 * A036247 A036248 A036249
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KEYWORD
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frac,nonn
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AUTHOR
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Jeff Burch
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STATUS
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approved
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