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%I #9 Apr 09 2022 06:39:48
%S 1,0,3,3,12,30,93,300,1038,3810,14781,60375,258807,1160949,5435652,
%T 26502555,134282406,705720549,3840542031,21608662710,125523530724,
%U 751831408929,4637611255422,29428408797852,191907975348210
%N a(n) = Sum_{k=0..floor(n/2)} Stirling2(n-k,k) * 3^k.
%H Seiichi Manyama, <a href="/A097342/b097342.txt">Table of n, a(n) for n = 0..647</a>
%F a(n)=sum{k=0..floor(n/2), sum{i=0..k, (-1)^(k+i)i^(n-k)/(i!(k-i)!)}3^k }
%F G.f.: Sum_{k>=0} 3^k * x^(2*k)/Product_{j=1..k} (1 - j * x). - _Seiichi Manyama_, Apr 09 2022
%t Table[Sum[StirlingS2[n-k,k]3^k,{k,0,Floor[n/2]}],{n,0,30}] (* _Harvey P. Dale_, May 24 2012 *)
%o (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
%o (PARI) a(n) = sum(k=0, n\2, 3^k*stirling(n-k, k, 2)); \\ _Seiichi Manyama_, Apr 09 2022
%Y Cf. A024427, A097341.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Aug 05 2004
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