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A192555
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a(n) = Sum_{k=0..n} Stirling2(n+1, k+1)*(-1)^(n-k)*k!^2.
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0
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1, 0, 2, 18, 302, 7770, 285182, 14169498, 916379102, 74833699770, 7532323742462, 916288114073178, 132533661862902302, 22482642651307262970, 4420834602574484743742, 997471931914411955132058, 255978001773528747607767902, 74137405656663750753878861370
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OFFSET
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0,3
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COMMENTS
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This sequence is the Akiyama-Tanigawa transform of the factorial numbers. - Peter Luschny, Apr 19 2024
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LINKS
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FORMULA
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MAPLE
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ATFactorial := proc(len)
local k, j, A, R, F; F := 1;
for k from 0 to len do
R[k] := F; F := F * (k + 1);
for j from k by -1 to 1 do
R[j - 1] := j * (R[j] - R[j-1])
od;
A[k] := R[0];
od; convert(A, list) end:
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MATHEMATICA
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Table[Sum[StirlingS2[n+1, k+1](-1)^(n-k)k!^2, {k, 0, n}], {n, 0, 100}]
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PROG
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(Maxima) makelist(sum(stirling2(n+1, k+1)*(-1)^(n-k)*k!^2, k, 0, n), n, 0, 24);
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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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