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A217391
Partial sums of the squares of the ordered Bell numbers (number of preferential arrangements) A000670.
4
1, 2, 11, 180, 5805, 298486, 22228975, 2258856824, 300194704049, 50529463186170, 10505093602625139, 2643441560563225468, 791779611505017309493, 278371498870260182630654, 113516551713466910954246903, 53143864598655784249290736512, 28309328562668956145157858372537
OFFSET
0,2
LINKS
FORMULA
a(n) = Sum_{k=0..n} t(k)^2 where t = A000670 (ordered Bell numbers).
a(n) ~ (n!)^2 / (4 * (log(2))^(2*n+2)). - Vaclav Kotesovec, Nov 08 2014
MATHEMATICA
t[n_] := Sum[StirlingS2[n, k]k!, {k, 0, n}]; Table[Sum[t[k]^2, {k, 0, n}], {n, 0, 100}]
PROG
(Maxima)
t(n):=sum(stirling2(n, k)*k!, k, 0, n);
makelist(sum(t(k)^2, k, 0, n), n, 0, 40);
(Magma)
A000670:=func<n | &+[StirlingSecond(n, i)*Factorial(i): i in [0..n]]>;
[&+[A000670(k)^2: k in [0..n]]: n in [0..14]]; // Bruno Berselli, Oct 03 2012
(PARI) for(n=0, 30, print1(sum(k=0, n, (sum(j=0, k, j!*stirling(k, j, 2)))^2), ", ")) \\ G. C. Greubel, Feb 07 2018
CROSSREFS
Partial sums of A122725.
Sequence in context: A012974 A011839 A271507 * A297601 A089760 A288556
KEYWORD
nonn
AUTHOR
Emanuele Munarini, Oct 02 2012
STATUS
approved