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A242283
a(n) = Sum_{k=0..n} (k!)^6 * StirlingS2(n,k)^3.
2
1, 1, 65, 48385, 201202625, 3177816192001, 149444281172914625, 17688550295661103160065, 4659004670032668841494537665, 2485460204094055083075883434816001, 2493268982658347340546535733064008565185, 4428569787044987118931586341533071670315481345
OFFSET
0,3
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).
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].
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}]
CROSSREFS
Cf. A064618 (p=1), A242282 (p=2).
Sequence in context: A103345 A291456 A269794 * A061688 A337808 A218689
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, May 10 2014
STATUS
approved