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A068518 The sequence S(n,-3,1,1), where S(r,k,t,q) is defined by Sum(0<=j<=r){combin(r+q,j)^t*B(j,k)} and B(j,k) is the j-th k-poly-Bernoulli number. 0
1, 17, 163, 1229, 8131, 49637, 287323, 1602989 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The sequence S(n,-2,1,1), n>=0, is A016269. It would be interesting to study the more general sequences S(r,-m,1,1), r=0,1,2,... for fixed m; here we consider the special cases m=3 and m=2. Finally, one can use the sum S(r,k,t,q) to discover certain recurrence relations involving poly-Bernoulli numbers. Let us note that the well known recurrence of the classical Bernoulli numbers yields S(r,1,1,1)=r+1. Let us also note that numerical experimentation suggests that S(r,-2,1,1)=S(r,-3,0,q).

LINKS

Table of n, a(n) for n=0..7.

FORMULA

S(r, -3, 1, 1)=Sum(0<=n<=r){combin(r+1, n)*[(-1)^n*Sum(0<=m<=n){(m+1)^2*Sum(0<=s<=m){(-1)^s*combin(m, s)*s^n}]}

CROSSREFS

Sequence in context: A198859 A160295 A125645 * A155664 A096192 A076458

Adjacent sequences:  A068515 A068516 A068517 * A068519 A068520 A068521

KEYWORD

nonn

AUTHOR

Vesselin Dimitrov (avding(AT)hotmail.com), Mar 18 2002

STATUS

approved

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Last modified March 20 05:17 EDT 2019. Contains 321344 sequences. (Running on oeis4.)