A217391 Partial sums of the squares of the ordered Bell numbers (number of preferential arrangements) A000670.

1, 2, 11, 180, 5805, 298486, 22228975, 2258856824, 300194704049, 50529463186170, 10505093602625139, 2643441560563225468, 791779611505017309493, 278371498870260182630654, 113516551713466910954246903, 53143864598655784249290736512, 28309328562668956145157858372537

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

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

Cf. A000670, A006957, A005649, A217388, A217389, A217392.

Partial sums of A122725.

Sequence in context: A012974 A011839 A271507 * A297601 A089760 A288556

Adjacent sequences: A217388 A217389 A217390 * A217392 A217393 A217394

Keyword

nonn

Author

Emanuele Munarini, Oct 02 2012

Status

approved