A346314 Sum_{n>=0} a(n) * x^n / (n!)^2 = Product_{n>=1} (1 - x^n / (n!)^2).

1, -1, -1, 8, 15, 124, -3340, -9311, -102641, -1880812, 150047424, 692058289, 8916106452, 167039809897, 7435628931289, -1381243302601067, -9407162843960561, -165954439670564988, -3103870029424074136, -123659189880256295879, -10671656695397289496160

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Formula

a(0) = 1; a(n) = -(1/n) * Sum_{k=1..n} (binomial(n,k) * k!)^2 * k * ( Sum_{d|k} 1 / (d * ((k/d)!)^(2*d)) ) * a(n-k).

Mathematica

nmax = 20; CoefficientList[Series[Product[(1 - x^k/(k!)^2), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!^2
a[0] = 1; a[n_] := a[n] = -(1/n) Sum[(Binomial[n, k] k!)^2 k Sum[1/(d ((k/d)!)^(2 d)), {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]

Crossrefs

Cf. A183229, A183240, A185895, A346315.

Sequence in context: A110294 A110459 A132374 * A361710 A234534 A067686

Adjacent sequences: A346311 A346312 A346313 * A346315 A346316 A346317

Keyword

sign

Author

Ilya Gutkovskiy, Jul 13 2021

Status

approved