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A053581
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First differences of the Poly-Bernoulli numbers B_n^(k) with k=-2 (A027649).
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4
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1, 3, 10, 32, 100, 308, 940, 2852, 8620, 25988, 78220, 235172, 706540, 2121668, 6369100, 19115492, 57362860, 172121348, 516429580, 1549419812, 4648521580, 13946089028, 41839315660, 125520044132
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also the second differences of A001047.
Contribution from Gary W. Adamson, Jun 04 2009: (Start)
Equals sum of "terms added" to current row of the triangle version of A038573 to get the next row.
a(3) = 32 sum of (3, 7, 7, 15) = terms appended to row 2 of the triangle in A038573. (End)
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
| a(n) = 5*a(n-1)-6*a(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.
Binomial transform of A00975(n+1). G.f.: (1-x)^2/((1-2*x)*(1-3*x)); a(n)=4*3^n/3+0^n/6-2^n/2. - Paul Barry, Jun 26 2003
a(n)=sum{k=0..n+1, C(n+1, k)*sum{j=0..floor(k/2), A001045(k-2j)}}; - Paul Barry, Apr 17 2005
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MATHEMATICA
| CoefficientList[Series[(1-x)^2/((1-2x)(1-3x)), {x, 0, 30}], x] (* From Harvey P. Dale, Apr 22 2011 *)
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PROG
| (MAGMA) [4*3^n/3+0^n/6-2^n/2: n in [0..30]]; // Vincenzo Librandi, Jul 17 2011
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CROSSREFS
| Cf. A001047 and A027649.
Cf. A001045.
A038573 [From Gary W. Adamson, Jun 04 2009]
Sequence in context: A036682 A104270 A038731 * A092822 A017935 A134377
Adjacent sequences: A053578 A053579 A053580 * A053582 A053583 A053584
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams, Jan 18 2000
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