0,2

Poly-Bernoulli numbers B_n^(k) with k=-2.

Binomial transform of A007051, if both sequences start at 0. Binomial transform of A000225(n+1). - Paul Barry (pbarry(AT)wit.ie), Mar 24 2003

Euler expands (1-z)/(1-5z+6z^2) and finds the general term. Section 226 of the Introductio indicates that he could have written down the recursion relation: a(n) = 5 a(n-1)-6 a(n-2). - V. Frederick Rickey (fred-rickey(AT)usma.edu), Feb 10 2006

Let R be a binary relation on the power set P(A) of a set A having n = |A| elements such that for every element x, y of P(A), xRy if x is a subset of y or y is a subset of x. Then a(n) = |R|. - Ross La Haye (rlahaye(AT)new.rr.com), Dec 22 2006 Ross

M. Kaneko, Poly-Bernoulli numbers, J. Theorie des Nombres Bordeaux 9 (1997), 221-228.

Leonhard Euler, Introduction in analysin infinitorum (1748), section 216.

T. D. Noe, Table of n, a(n) for n=0..200

Index entries for sequences related to Bernoulli numbers.

M. Kaneko, Poly-Bernoulli numbers

G.f.: (1-x)/((1-2*x)*(1-3*x)). a(0)=1, a(n)=3*a(n-1)+2^(n-1).

a(n)=sum{k=0..n, C(n, k)(2^(k + 1) - 1)}. - Paul Barry (pbarry(AT)wit.ie), Mar 24 2003

Partial sums of A053581. - Paul Barry (pbarry(AT)wit.ie), Jun 26 2003

Main diagonal of array (A085870) defined by T(i, 1)=2^i-1, T(1, j)=2^j-1, T(i, j)=T(i-1, j)+T(i-1, j-1). - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 05 2003

a(n) = A090888(n, 3). - Ross La Haye (rlahaye(AT)new.rr.com), Sep 21 2004

a(n)=sum{k=0..n, C(n+2, k+1)*sum{j=0..floor(k/2), A001045(k-2j)}} - Paul Barry (pbarry(AT)wit.ie), Apr 17 2005

a(n)=sum{k=0..n, sum{j=0..n, C(n,j)C(j+1,k+1)}}; - Paul Barry (pbarry(AT)wit.ie), Sep 18 2006

Row sums of triangle A131109. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 15 2007

(-1)^n*sum( (-1)^'m'*'m'!*stirling2(n, 'm')/('m'+1)^k, 'm'=0..n);

Row 2 of array A099594.

Cf. A131109.

Sequence in context: A029868 A030267 A026290 this_sequence A049221 A081670 A124805

Adjacent sequences: A027646 A027647 A027648 this_sequence A027650 A027651 A027652

nonn,easy,nice

njas

Better formulae from David W. Wilson (davidwwilson(AT)comcast.net) and Michael Somos.