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 A354311 Expansion of e.g.f. exp( x/2 * (exp(2 * x) - 1) ). 3
 1, 0, 2, 6, 28, 160, 1056, 7784, 63568, 569664, 5542240, 58038112, 650045760, 7746901760, 97790608384, 1302349549440, 18235836899584, 267663541270528, 4107395264113152, 65739857693144576, 1095095457262013440, 18949711553467957248, 340036076121127395328 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..22. FORMULA a(0) = 1; a(n) = Sum_{k=2..n} k * 2^(k-2) * binomial(n-1,k-1) * a(n-k). a(n) = n! * Sum_{k=0..floor(n/2)} 2^(n-2*k) * Stirling2(n-k,k)/(n-k)!. PROG (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x/2*(exp(2*x)-1)))) (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j*2^(j-2)*binomial(i-1, j-1)*v[i-j+1])); v; (PARI) a(n) = n!*sum(k=0, n\2, 2^(n-2*k)*stirling(n-k, k, 2)/(n-k)!); CROSSREFS Cf. A052506, A354312. Cf. A351733, A351736, A354309, A354313. Sequence in context: A277381 A184695 A086633 * A201950 A358265 A356633 Adjacent sequences: A354308 A354309 A354310 * A354312 A354313 A354314 KEYWORD sign AUTHOR Seiichi Manyama, May 23 2022 STATUS approved

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Last modified May 21 21:53 EDT 2024. Contains 372738 sequences. (Running on oeis4.)