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A242282 Sum_{k=0..n} (k!)^4 * StirlingS2(n,k)^2. 3
1, 1, 17, 1441, 379217, 241351201, 316806826577, 767860003562401, 3168021900014798417, 20904944903800508800801, 210024043938800961464262737, 3086813642229865705833791897761, 64215498113561436496993921529947217 (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..12.

FORMULA

a(n) ~ c * (n!)^4, where c = BesselI(0,1) = 1.266065877752... (see A197036).

MATHEMATICA

Table[Sum[(k!)^4 * StirlingS2[n, k]^2, {k, 0, n}], {n, 0, 20}]

CROSSREFS

Cf. A064618 (p=1), A242283 (p=3).

Cf. A197036.

Sequence in context: A256020 A072160 A078814 * A129911 A104808 A061686

Adjacent sequences:  A242279 A242280 A242281 * A242283 A242284 A242285

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, May 10 2014

STATUS

approved

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Last modified March 25 20:10 EDT 2019. Contains 321477 sequences. (Running on oeis4.)