login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A087650 a(n) = Sum_{k=0..n} (-1)^(n-k)*Bell(k). 5
1, 0, 2, 3, 12, 40, 163, 714, 3426, 17721, 98254, 580316, 3633281, 24011156, 166888166, 1216070379, 9264071768, 73600798036, 608476008123, 5224266196934, 46499892038438, 428369924118313, 4078345814329010, 40073660040755336 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) is the number of set partitions of [n] that contain exactly one singleton block and all other blocks contain an entry > this singleton. For example, a(3)=3 counts 124/3, 134/2, 1/234 but not 123/4. - David Callan, Aug 27 2014

Partial sums are A173109. - Vladimir Reshetnikov, Oct 29 2015

LINKS

Table of n, a(n) for n=0..23.

FORMULA

E.g.f.: exp(-x)*((exp(x)-1)*exp(exp(x)-1)+1).

a(n) = (-1)^n + Bell(n) - A000296(n), with Bell(n)=A000110(n). - Wolfdieter Lang, Dec 01 2003

a(n) = A000296(n+1) + (-1)^n. - David Callan, Aug 27 2014

G.f.: 1/(1+x)/W(0), where W(k) = 1 - x/(1 - x*(k+1)/W(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Nov 10 2014

EXAMPLE

G.f. = 1 + 2*x^2 + 3*x^3 + 12*x^4 + 40*x^5 + 163*x^6 + 714*x^7 + ...

MATHEMATICA

f[n_] := Sum[ StirlingS2[n, k], {k, 1, n}]; Table[(-1)^n + Sum[(-1)^(n - k)*f[k], {k, 0, n}], {n, 0, 23}] (* Robert G. Wilson v *)

Needs["DiscreteMath`Combinatorica`"]; Table[ Sum[(-1)^(n - k)*BellB[k], {k, 0, n}], {n, 0, 23}] (* Robert G. Wilson v *)

PROG

(Maxima) makelist(sum((-1)^(n-k)*belln(k), k, 0, n), n, 0, 40); // Emanuele Munarini, Sep 27 2012

(Sage)

def A087650_list(len): # After the formula of David Callan.

    if len == 1: return [1]

    if len == 2: return [1, 0]

    R = []; A = [1]; p = -1

    for i in (0..len-1):

        A.append(A[0] - A[i])

        A[i] = A[0]

        for k in range(i, 0, -1):

            A[k-1] += A[k]

        p = -p

        R.append(A[i+1] + p)

    return R

A087650_list(24) # Peter Luschny, Aug 28 2014

(PARI) vector(30, n, n--; sum(k=0, n, (-1)^(n-k)*polcoeff(sum(i=0, k, prod( j=1, i, x / (1 - j*x)), x^k * O(x)), k))) \\ Altug Alkan, Oct 30 2015

CROSSREFS

Cf. A000110, A000296, A005001, A005493, A173109.

Sequence in context: A012310 A082526 A151368 * A177699 A256881 A012514

Adjacent sequences:  A087647 A087648 A087649 * A087651 A087652 A087653

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Sep 23 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 7 19:05 EST 2016. Contains 278895 sequences.