A384086 a(n) = [x^n] Product_{k=1..n} ((1 + k*x)/(1 - k*x))^2.

1, 4, 72, 2352, 112000, 7023540, 546991704, 50923706176, 5517464159232, 682067031126660, 94744306830613000, 14610279918692775504, 2476682373835289303424, 457771369968515293229812, 91624876032673265663215800, 19743379886572250897986694400, 4556982707091255612929249419264

Offset: 0

Author

Vaclav Kotesovec, May 19 2025

Keywords

• nonn

Crossrefs

Cf. A129256, A350376.

Cf. A350366, A384087, A384088, A351764.

Programs

Mathematica

Table[SeriesCoefficient[Product[(1+k*x)^2/(1-k*x)^2, {k, 1, n}], {x, 0, n}], {n, 0, 20}]

Formula

a(n) ~ c * d^n * n! / n, where d = 15.357995623209995052090556511543938190953157405669200... and c = 0.3746298100044008083790505105262276548713201624206421...