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A217389 Partial sums of the ordered Bell numbers (number of preferential arrangements) A000670. 8
1, 2, 5, 18, 93, 634, 5317, 52610, 598445, 7685706, 109933269, 1732565842, 29824133437, 556682481818, 11198025452261, 241481216430114, 5557135898411469, 135927902927547370, 3521462566184392693, 96323049885512803826 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

a(n) = Sum_{k=0..n} t(k), where t = A000670 (ordered Bell numbers).

G.f. = A(x)/(1-x), where A(x) = g.f. for A000670 (see that entry). - N. J. A. Sloane, Apr 12 2014

a(n) ~ n! / (2* (log(2))^(n+1)). - Vaclav Kotesovec, Nov 08 2014

MATHEMATICA

t[n_] := Sum[StirlingS2[n, k]k!, {k, 0, n}]; Table[Sum[t[k], {k, 0, n}], {n, 0, 100}]

(* second program: *)

Fubini[n_, r_] := Sum[k!*Sum[(-1)^(i+k+r)(i+r)^(n-r)/(i!*(k-i-r)!), {i, 0, k-r}], {k, r, n}]; Fubini[0, 1] = 1; Table[Fubini[n, 1], {n, 0, 20}] // Accumulate (* Jean-Fran├žois Alcover, Mar 31 2016 *)

PROG

(Maxima)

t(n):=sum(stirling2(n, k)*k!, k, 0, n);

makelist(sum(t(k), k, 0, n), n, 0, 40);

(MAGMA)

A000670:=func<n | &+[StirlingSecond(n, i)*Factorial(i): i in [0..n]]>;

[&+[A000670(k): k in [0..n]]: n in [0..19]]; // Bruno Berselli, Oct 03 2012

(PARI) for(n=0, 30, print1(sum(k=0, n, sum(j=0, k, j!*stirling(k, j, 2))), ", ")) \\ G. C. Greubel, Feb 07 2018

CROSSREFS

Cf. A000670, A006957, A005649, A217388, A217391, A217392.

See A239914 for another version.

Sequence in context: A320154 A032273 A143522 * A123310 A058119 A335547

Adjacent sequences:  A217386 A217387 A217388 * A217390 A217391 A217392

KEYWORD

nonn

AUTHOR

Emanuele Munarini, Oct 02 2012

STATUS

approved

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Last modified October 28 04:43 EDT 2021. Contains 348313 sequences. (Running on oeis4.)