A292312 Expansion of Product_{k>=1} (1 - k^k*x^k).

1, -1, -4, -23, -229, -2761, -42615, -758499, -15702086, -365588036, -9516954786, -273061566624, -8575969258607, -292418459301779, -10762887030763337, -425243370397722674, -17953905924215881215, -806666656048846472309

Offset: 0

Author

Seiichi Manyama, Sep 14 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..386

Crossrefs

Column k=1 of A294653.

Cf. A023882, A265949.

Programs

Magma

m:=20; R:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[(1 - k^k*x^k): k in [1..m]]) )); // G. C. Greubel, Oct 31 2018

Maple

seq(coeff(series(mul((1-k^k*x^k),k=1..n),x,n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 31 2018

Mathematica

terms = 18; CoefficientList[Product[(1 - k^k*x^k), {k, 1, terms}] + O[x]^(terms), x] (* Jean-François Alcover, Nov 11 2017 *)

PARI

{a(n) = polcoeff(prod(k=1, n, 1-k^k*x^k+x*O(x^n)), n)}

Formula

Convolution inverse of A023882.

a(n) ~ -n^n * (1 - exp(-1)/n - (exp(-1)/2 + 4*exp(-2))/n^2). - Vaclav Kotesovec, Sep 14 2017

a(0) = 1 and a(n) = -(1/n) * Sum_{k=1..n} A294645(k)*a(n-k) for n > 0. - Seiichi Manyama, Nov 09 2017