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A356394
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Expansion of e.g.f. ( Product_{k>0} (1+x^k)^k )^(1/(1-x)).
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6
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1, 1, 6, 51, 452, 5210, 68514, 1032906, 17352320, 323948376, 6594052680, 145585638000, 3461441121192, 88092914635128, 2388119359650192, 68667743686492440, 2086307088847714560, 66762608893508354880, 2243693428523140377024, 78982154604162553529664
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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(0) = 1; a(n) = Sum_{k=1..n} A356391(k) * binomial(n-1,k-1) * a(n-k).
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MATHEMATICA
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nmax = 20; CoefficientList[Series[Product[(1+x^k)^k, {k, 1, nmax}]^(1/(1-x)), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Aug 07 2022 *)
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PROG
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(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(prod(k=1, N, (1+x^k)^k)^(1/(1-x))))
(PARI) a356391(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(k/d+1)*d^2)/k);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356391(j)*binomial(i-1, j-1)*v[i-j+1])); v;
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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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