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URL: https://oeis.org/A329259

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A329259
Expansion of e.g.f. -log(1 - Sum_{k>=1} x^(k^2) / (k^2)!).
1
0, 1, 1, 2, 7, 29, 150, 930, 6755, 56071, 523540, 5430710, 61967070, 771361525, 10402051660, 151065164250, 2350567168951, 39013029955917, 687979755287416, 12845920452293594, 253183788618567525, 5252704310496986070, 114424576082127987830, 2611313756103949479660
OFFSET
0,4
FORMULA
a(0) = 0; a(n) = A010052(n) + (1/n) * Sum_{k=1..n-1} binomial(n,k) * A010052(n-k) * k * a(k).
MATHEMATICA
nmax = 23; CoefficientList[Series[-Log[1 - Sum[x^(k^2)/(k^2)!, {k, 1, Floor[nmax^(1/2)] + 1}]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Boole[IntegerQ[n^(1/2)]] + Sum[Binomial[n, k] Boole[IntegerQ[(n - k)^(1/2)]] k a[k], {k, 1, n - 1}]/n; a[0] = 0; Table[a[n], {n, 0, 23}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 09 2019
STATUS
approved