A242283 a(n) = Sum_{k=0..n} (k!)^6 * StirlingS2(n,k)^3.

1, 1, 65, 48385, 201202625, 3177816192001, 149444281172914625, 17688550295661103160065, 4659004670032668841494537665, 2485460204094055083075883434816001, 2493268982658347340546535733064008565185, 4428569787044987118931586341533071670315481345

Offset: 0

Author

Vaclav Kotesovec, May 10 2014

Keywords

• nonn
• easy

Comments

Generally, for p>=1 is Sum_{k=0..n} (k!)^(2*p) * StirlingS2(n,k)^p asymptotic to c * (n!)^(2*p), where c = 1 + Sum_{n>=1} 1/(Product_{k=1..n} (2*k)^p).

Crossrefs

Cf. A064618 (p=1), A242282 (p=2).

Programs

Maple

a:= n-> add(k!^6*Stirling2(n,k)^3, k=0..n):
seq(a(n), n=0..15);  # Alois P. Heinz, Oct 23 2023

Mathematica

Table[Sum[(k!)^6 * StirlingS2[n,k]^3,{k,0,n}],{n,0,20}]

Formula

a(n) ~ c * (n!)^6, where c = 1.1269621849236767... = 1 + Sum_{n>=1} 1/(Product_{k=1..n} (2*k)^3) = HypergeometricPFQ[{}, {1, 1}, 1/8].