A329259 Expansion of e.g.f. -log(1 - Sum_{k>=1} x^(k^2) / (k^2)!).

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

Links

Table of n, a(n) for n=0..23.

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

Cf. A000629, A010052, A205803, A205804, A329256, A329258.

Sequence in context: A030920 A030824 A030956 * A185310 A143883 A346427

Adjacent sequences: A329256 A329257 A329258 * A329260 A329261 A329262

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 09 2019

Status

approved