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A097342
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a(n) = Sum_{k=0..floor(n/2)} Stirling2(n-k,k) * 3^k.
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7
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1, 0, 3, 3, 12, 30, 93, 300, 1038, 3810, 14781, 60375, 258807, 1160949, 5435652, 26502555, 134282406, 705720549, 3840542031, 21608662710, 125523530724, 751831408929, 4637611255422, 29428408797852, 191907975348210
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n)=sum{k=0..floor(n/2), sum{i=0..k, (-1)^(k+i)i^(n-k)/(i!(k-i)!)}3^k }
G.f.: Sum_{k>=0} 3^k * x^(2*k)/Product_{j=1..k} (1 - j * x). - Seiichi Manyama, Apr 09 2022
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MATHEMATICA
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Table[Sum[StirlingS2[n-k, k]3^k, {k, 0, Floor[n/2]}], {n, 0, 30}] (* Harvey P. Dale, May 24 2012 *)
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PROG
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(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, 3^k*x^(2*k)/prod(j=1, k, 1-j*x))) \\ Seiichi Manyama, Apr 09 2022
(PARI) a(n) = sum(k=0, n\2, 3^k*stirling(n-k, k, 2)); \\ Seiichi Manyama, Apr 09 2022
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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