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A326651
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a(n) = Sum_{k>0} k * A326616(k,n).
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3
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0, 1, 14, 243, 9692, 865445, 196868202, 122831606807, 219073289264824, 1139077903664789577, 17597009238919048388550, 821444189426979675481201211, 116802449602563244067365434335892, 50816512870344533477388136382624158445
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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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MAPLE
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g:= proc(n) option remember; `if`(n=0, 0, numtheory[sigma](n)+g(n-1)) end:
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add((t->
b(n-t, min(n-t, i-1), k)*binomial(k, t))(i*j), j=0..n/i)))
end:
a:= k-> add(n*add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k), n=k..g(k)):
seq(a(n), n=0..15);
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MATHEMATICA
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g[n_] := g[n] = If[n == 0, 0, DivisorSigma[1, n] + g[n - 1]];
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[With[{t = i*j}, b[n - t, Min[n - t, i - 1], k]*Binomial[k, t]], {j, 0, n/i}]]];
a[k_] := Sum[n*Sum[b[n, n, k - i]*(-1)^i*Binomial[k, i], {i, 0, k}], {n, k, g[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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