A242280 a(n) = Sum_{k=0..n} (k!*StirlingS2(n,k))^3.

1, 1, 9, 433, 63225, 18954001, 10159366329, 8924902306993, 11969476975085625, 23232038620328946001, 62655369716047066046649, 227268291642918880258797553, 1079475019974966974009683584825, 6565863403062578428919598754170001

Offset

0,3

Comments

Generally, for p>=1 is Sum_{k=0..n} (k!*StirlingS2(n,k))^p asymptotic to n^(p*n+1/2) * sqrt(Pi/(2*p*(1-log(2))^(p-1))) / (exp(p*n) * log(2)^(p*n+1)).

Links

G. C. Greubel, Table of n, a(n) for n = 0..169

Formula

a(n) ~ sqrt(Pi/6) * n^(3*n+1/2) / ((1-log(2)) * exp(3*n) * (log(2))^(3*n+1)).

Mathematica

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

Crossrefs

Cf. A000670, A048144.

Sequence in context: A271652 A156092 A092813 * A266294 A273889 A167720

Adjacent sequences: A242277 A242278 A242279 * A242281 A242282 A242283

Keyword

nonn,easy

Author

Vaclav Kotesovec, May 10 2014

Status

approved