A382979 a(n) = [(x*y)^n] Product_{k>=1} 1/(1 - x^k + y^k).

1, -2, 4, -20, 78, -282, 1048, -4014, 15456, -59224, 227646, -879694, 3407730, -13219372, 51375286, -200021556, 779870542, -3044448644, 11898709560, -46553635346, 182315752476, -714619687038, 2803342734160, -11005274516610, 43233909672938, -169951684067602, 668474115081988

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Formula

a(n) ~ (-1)^n * 4^n / (A100221 * sqrt(Pi*n)). - Vaclav Kotesovec, Apr 13 2025

Mathematica

a[n_]:=SeriesCoefficient[Product[1/(1-x^k+y^k), {k, 1, n+5}], {x, 0, n}, {y, 0, n}]; Table[a[n], {n, 0, 26}] (* Vincenzo Librandi, Apr 12 2025 *)

Prog

(Magma) nmax := 26; prec := 2*nmax + 10; Rx<x> := PowerSeriesRing(Rationals(), prec); Rxy<y> := PowerSeriesRing(Rx, prec); P := Rxy!1; for k in [1..prec] do P *:= 1/(1 - x^k + y^k); end for; seq := [Coefficient(Coefficient(P, n), n) : n in [0..nmax]]; print seq; // Vincenzo Librandi, Apr 12 2025

Crossrefs

Main diagonal of A382974.

Cf. A322211, A100221.

Sequence in context: A204550 A009291 A081440 * A204438 A325791 A188326

Adjacent sequences: A382976 A382977 A382978 * A382980 A382981 A382982

Keyword

sign

Author

Seiichi Manyama, Apr 11 2025

Status

approved