A326865 G.f.: Product_{k>=1} (1 + x^k/k^3) = Sum_{n>=0} a(n)*x^n/n!^3.

1, 1, 1, 35, 728, 48824, 7170984, 1418111064, 479963197440, 235727037775872, 170423013422592000, 163854260184125952000, 214343327259234349056000, 360795240553638133592064000, 778954481701636984110452736000, 2095759092922096320907078496256000

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..182

Formula

a(n) ~ c * (n-1)!^3, where c = A073017 = Product_{k>=1} (1 + 1/k^3) = cosh(sqrt(3)*Pi/2)/Pi = 2.428189792098870328736...

Maple

b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0, 1,
      b(n, i-1)+b(n-i, min(n-i, i-1))*((i-1)!*binomial(n, i))^3))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..20);  # Alois P. Heinz, Jul 27 2023

Mathematica

nmax = 20; CoefficientList[Series[Product[(1+x^k/k^3), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!^3

Crossrefs

Cf. A007838, A249593, A326864.

Sequence in context: A367250 A278361 A145603 * A139641 A240928 A028220

Adjacent sequences: A326862 A326863 A326864 * A326866 A326867 A326868

Keyword

nonn

Author

Vaclav Kotesovec, Jul 27 2019

Status

approved