A386729 a(n) = [x^n] G(x)^n, where G(x) = Product_{k >= 1} (1 + x^k)^(k^3) is the g.f. of A248882.

1, 1, 17, 154, 1377, 13276, 127862, 1249746, 12321121, 122287798, 1220492192, 12235940113, 123133325382, 1243080020352, 12583773308102, 127688996851804, 1298370095026017, 13226355435367992, 134955405683954234, 1379032238329708409, 14110075394718902752, 144544237021110644340

Offset: 0

Author

Vaclav Kotesovec, Jul 31 2025

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..975

Crossrefs

Cf. A248882, A284900, A386720.

Cf. A270913, A270922, A380291.

Programs

Mathematica

Table[SeriesCoefficient[Product[(1+x^k)^(n*k^3), {k, 1, n}], {x, 0, n}], {n, 0, 25}]
Table[SeriesCoefficient[Exp[n*Sum[Sum[(-1)^(k/d + 1)*d^4, {d, Divisors[k]}]*x^k/k, {k, 1, n}]], {x, 0, n}], {n, 0, 25}]

Formula

a(n) = [x^n] exp(n*Sum_{k >= 1} s_4(k)*x^k/k), where s_4(n) = Sum_{d divides n} (-1)^(n/d+1)*d^4 = A284900(n).

a(n) ~ c * d^n / sqrt(n), where d = 10.49088673566991578441632677715184699104285539252671173854512548234581416... and c = 0.2449508761900081824436717230940007974244164508939377916825513986093942...