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A082430
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a(1)=1; for n > 1, a(n) = n*(a(n-1) + a(n-2) + ... + a(2) + a(1)) + 4.
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1
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1, 6, 25, 132, 824, 5932, 48444, 442916, 4484524, 49828044, 602919332, 7892762164, 111156400476, 1675896499484, 26934050884564, 459674468429892, 8302870086014924, 158242935756990316, 3173649989348528004
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OFFSET
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1,2
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COMMENTS
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More generally, if m is an integer and a(1)=1, a(n) = n*(a(n-1) + a(n-2) + ... + a(2) + a(1)) + m then a(n) has a closed form formula as a(n) = floor/ceiling(n*r(m)*n!) where r(m) = frac(e*m) + 0 or + 1/2 or -1/2 + integer. (See Example section.)
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LINKS
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FORMULA
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For n >= 2, a(n) = ceiling(n*(19/2 - 4*e)*n!).
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EXAMPLE
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r(10) = frac(10*e) + 1/2 + 2;
r(12) = frac(12*e) - 1/2 + 3;
r(15) = frac(15*e) + 3;
r(18) = frac(18*e) - 1/2 + 4.
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MATHEMATICA
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nxt[{n_, t_, a_}]:=Module[{c=t(n+1)+4}, {n+1, t+c, c}]; NestList[nxt, {1, 1, 1}, 20][[;; , 3]] (* Harvey P. Dale, Mar 28 2024 *)
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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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