Search: id:A053581
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%I A053581
%S A053581 1,3,10,32,100,308,940,2852,8620,25988,78220,235172,706540,2121668,
%T A053581 6369100,19115492,57362860,172121348,516429580,1549419812,4648521580,
%U A053581 13946089028,41839315660,125520044132
%N A053581 First differences of the Poly-Bernoulli numbers B_n^(k) with k=-2 (A027649).
%C A053581 Also the second differences of A001047.
%C A053581 Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 04 2009: 
               (Start)
%C A053581 Equals sum of "terms added" to current row of the triangle version of 
               A038573 to get the next row.
%C A053581 a(3) = 32 sum of (3, 7, 7, 15) = terms appended to row 2 of the triangle 
               in A038573. (End)
%F A053581 a(n)=5a(n-1)-6a(n-2)+C(2, 2-n), n>1; a(0)=1, a(1)=3, where C(2, 2-n)=1 
               for n=2 and =0 for n>2.
%F A053581 Binomial transform of A00975(n+1). G.f.: (1-x)^2/((1-2x)(1-3x)); a(n)=4*3^n/
               3+0^n/6-2^n/2. - Paul Barry (pbarry(AT)wit.ie), Jun 26 2003
%F A053581 a(n)=sum{k=0..n+1, C(n+1, k)*sum{j=0..floor(k/2), A001045(k-2j)}}; - 
               Paul Barry (pbarry(AT)wit.ie), Apr 17 2005
%Y A053581 Cf. A001047 and A027649.
%Y A053581 Cf. A001045.
%Y A053581 A038573 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 04 2009]
%Y A053581 Sequence in context: A036682 A104270 A038731 this_sequence A092822 A017935 
               A134377
%Y A053581 Adjacent sequences: A053578 A053579 A053580 this_sequence A053582 A053583 
               A053584
%K A053581 easy,nonn
%O A053581 0,2
%A A053581 Barry E. Williams, Jan 18 2000

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