A292567 a(n) = [x^n] 1/(1+n*x) * Product_{j=2..n} 1/(1-x^j).

1, -1, 5, -29, 270, -3233, 47800, -838561, 17013991, -391779640, 10091836632, -287491284748, 8973657413421, -304549220113387, 11165193890312790, -439726629957500944, 18514829984975265703, -829953080825411342745, 39461813340364709540008

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..386

Formula

a(n) ~ (-1)^n * n^n * (1 + 1/n^2 - 1/n^3 + 2/n^4 - 2/n^5 + 4/n^6 - 4/n^7 + 7/n^8 - 8/n^9 + 12/n^10), for coefficients see A002865. - Vaclav Kotesovec, Sep 19 2017

Maple

b:= proc(n, i, k) option remember; `if`(n=0 or i=1, (-k)^n,
      `if`(i>n, 0, b(n-i, i, k))+b(n, i-1, k))
    end:
a:= n-> b(n$3):
seq(a(n), n=0..23);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0 || i == 1, (-k)^n, If[i > n, 0, b[n - i, i, k]] + b[n, i - 1, k]];
a[n_] := If[n == 0, 1, b[n, n, n]];
a /@ Range[0, 23] (* Jean-François Alcover, Dec 30 2020, after Alois P. Heinz *)

Crossrefs

Cf. A002865, A292462.

Sequence in context: A228387 A181356 A177440 * A355376 A332517 A332469

Adjacent sequences: A292564 A292565 A292566 * A292568 A292569 A292570

Keyword

sign

Author

Alois P. Heinz, Sep 19 2017

Status

approved