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A085350
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Binomial transform of poly-Bernoulli numbers A027649.
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8
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1, 5, 23, 101, 431, 1805, 7463, 30581, 124511, 504605, 2038103, 8211461, 33022991, 132623405, 532087943, 2133134741, 8546887871, 34230598205, 137051532983, 548593552421, 2195536471151, 8785632669005, 35152991029223
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: (1-2x)/((1-3x)(1-4x)).
E.g.f.: 2exp(4x) - exp(3x).
a(n) = 2*4^n-3^n.
a(n) = 4*a(n-1) + 9*a(n-2) - 36*a(n-3);
a(n) = 4*a(n-1) + 3^(n-1), both like A005061 (note for A005061 dual formula a(n) = 3*a(n-1) + 4^(n-1) = 3*a(n-1) + A000302(n-1)).
a(n) = 3*a(n-1) + 2^(2n+1) = 3*a(n-1) + A004171(n).
b(n) = mix(A005061, A085350) = 0,1,1,5,7,23,... = differences of (A167762 = 0,0,1,2,7,14,37,...); b(n) differences = A167784. (End)
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MATHEMATICA
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LinearRecurrence[{4, 9, -36}, {1, 5, 23}, 30] (* Harvey P. Dale, Nov 30 2011 *)
LinearRecurrence[{7, -12}, {1, 5}, 23] (* Ray Chandler, Aug 03 2015 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn,changed
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AUTHOR
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STATUS
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approved
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