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 A242283 Sum_{k=0..n} (k!)^6 * StirlingS2(n,k)^3. 2
 1, 1, 65, 48385, 201202625, 3177816192001, 149444281172914625, 17688550295661103160065, 4659004670032668841494537665, 2485460204094055083075883434816001, 2493268982658347340546535733064008565185 (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 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]. 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 A218689 A171706 Adjacent sequences:  A242280 A242281 A242282 * A242284 A242285 A242286 KEYWORD nonn,easy AUTHOR Vaclav Kotesovec, May 10 2014 STATUS approved

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Last modified March 29 13:45 EDT 2020. Contains 333107 sequences. (Running on oeis4.)