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A119430
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Expansion of Sum_{k>=0} 2^k*x^(2k)/Product_{j=1..k} (1 - j*2x).
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2
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1, 0, 2, 4, 12, 40, 152, 640, 2928, 14400, 75744, 424640, 2527552, 15902848, 105313408, 731376640, 5311088896, 40233525248, 317296341504, 2600091120640, 22099119279104, 194487001540608, 1769555559897088, 16622286300921856
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OFFSET
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0,3
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..579
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FORMULA
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a(n) = Sum_{k=0..n} S2(k,n-k)*2^k where S2(n,k)=A048993(n,k);
a(n) = Sum_{k=0..floor(n/2)} S2(n-k,k)*2^(n-k).
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MATHEMATICA
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a[n_] := Sum[2^(n-k) * StirlingS2[n - k, k], {k, 0, Floor[n/2]}]; Array[a, 25, 0] (* Amiram Eldar, Apr 09 2022 *)
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PROG
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(PARI) a(n) = sum(k=0, n\2, 2^(n-k)*stirling(n-k, k, 2)); \\ Seiichi Manyama, Apr 08 2022
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CROSSREFS
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Cf. A004211, A048993, A119429.
Sequence in context: A204678 A025227 A211965 * A074034 A268952 A215072
Adjacent sequences: A119427 A119428 A119429 * A119431 A119432 A119433
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, May 19 2006
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STATUS
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approved
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