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A346395
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Expanison of e.g.f. -log(1 - x) * exp(3*x).
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4
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0, 1, 7, 38, 192, 969, 5115, 29322, 187992, 1370745, 11392839, 107043606, 1122823944, 12989320785, 164040593067, 2243143392138, 32994768719376, 519229765892241, 8701862242296807, 154700700117472422, 2907409255935736752, 57588370882960384377, 1198954118077558162875
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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) = n! * Sum_{k=0..n-1} 3^k / ((n-k) * k!).
a(0) = 0, a(1) = 1, a(n) = (n+2) * a(n-1) - 3 * (n-1) * a(n-2) + 3^(n-1). - Seiichi Manyama, May 27 2022
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MATHEMATICA
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nmax = 22; CoefficientList[Series[-Log[1 - x] Exp[3 x], {x, 0, nmax}], x] Range[0, nmax]!
Table[n! Sum[3^k/((n - k) k!), {k, 0, n - 1}], {n, 0, 22}]
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PROG
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(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=0; v[2]=1; for(i=2, n, v[i+1]=(i+2)*v[i]-3*(i-1)*v[i-1]+3^(i-1)); v; \\ Seiichi Manyama, May 27 2022
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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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