A269791 G.f.: Product_{n>=1} 1/(1 - x^n/n^4) = Sum_{n>=0} a(n)*x^n/n!^4.

1, 1, 17, 1393, 359200, 224991776, 291968881696, 701412781560352, 2873957814268080128, 18859650596161401139200, 188619789441121624152354816, 2761804817165898231731040301056, 57271995555712767650976765232545792, 1635810412682066454426684822491878391808

Offset: 0

Author

Vaclav Kotesovec, Mar 05 2016

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..140

Crossrefs

Cf. A007841, A249588, A249593, A269793, A269794.

Programs

Mathematica

Table[n!^4 * SeriesCoefficient[Product[1/(1 - x^k/k^4), {k, 1, n}], {x, 0, n}], {n, 0, 20}]

PARI

{a(n)=n!^4*polcoeff(prod(k=1, n, 1/(1-x^k/k^4 +x*O(x^n))), n)}
for(n=0, 20, print1(a(n), ", "))

Formula

a(n) ~ c * n!^4, where c = Product_{k>=2} 1/(1-1/k^4) = 4*Pi/sinh(Pi) = 4*A090986 = 1.08811621992853265180094633468815...