A346312 Sum_{n>=0} a(n) * x^n / (n!)^2 = Product_{n>=1} (1 - x^n / n^2).

1, -1, -1, 5, 28, 724, 36, 220716, -1255680, 110979072, 2530310400, 1193835283200, -24457819622400, 21656019855744000, 899271273253248000, 474367063601421849600, 45822442913828595302400, 28365278076547150440038400, 2614371018285307258994688000

Offset

0,4

Links

Table of n, a(n) for n=0..18.

Formula

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

Mathematica

nmax = 18; 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 Sum[1/(k/d)^(2 d - 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]

Crossrefs

Cf. A249588, A292359, A326864, A346313.

Sequence in context: A308593 A249784 A359649 * A359739 A344464 A348393

Adjacent sequences: A346309 A346310 A346311 * A346313 A346314 A346315

Keyword

sign

Author

Ilya Gutkovskiy, Jul 13 2021

Status

approved