A242283 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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).

LINKS

Table of n, a(n) for n=0..11.

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

Adjacent sequences: A242280 A242281 A242282 * A242284 A242285 A242286

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, May 10 2014

STATUS

approved