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A360727
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Expansion of Sum_{k>=0} (k * x * (1 + x^2))^k.
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5
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1, 1, 4, 28, 264, 3206, 47684, 839249, 17058688, 393216567, 10134918592, 288815780665, 9016571143680, 306027510946208, 11219450971161024, 441846991480590475, 18602901833071633792, 833832341625621777368, 39642569136740054367808
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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/3)} (n-2*k)^(n-2*k) * binomial(n-2*k,k).
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MATHEMATICA
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nmax = 20; CoefficientList[1 + Series[Sum[(k*x*(1 + x^2))^k, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 18 2023 *)
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PROG
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(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x*(1+x^2))^k))
(PARI) a(n) = sum(k=0, n\3, (n-2*k)^(n-2*k)*binomial(n-2*k, k));
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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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