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 A081674 Generalized Poly-Bernoulli numbers. 3
 0, 1, 6, 29, 130, 561, 2366, 9829, 40410, 164921, 669526, 2707629, 10919090, 43942081, 176565486, 708653429, 2841788170, 11388676041, 45619274246, 182670807229, 731264359650, 2926800830801, 11712433499806, 46865424529029 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Binomial transform of A027649. Inverse binomial transform of A081675 With offset 1, partial sums of A085350. - Paul Barry, Jun 24 2003 Number of walks of length 2n+2 between two nodes at distance 4 in the cycle graph C_12. - Herbert Kociemba, Jul 05 2004 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (8,-19,12). FORMULA a(n) = ((4^(n+1) - 1)/3 - 3^n)/2 = (4*4^n - 3*3^n - 1)/6. a(n) = (A002450(n+1) + A000244(n))/2. G.f.: x*(1-2*x)/((1-x)*(1-3*x)*(1-4*x)). MATHEMATICA Join[{a=0, b=1}, Table[c=7*b-12*a-1; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 19 2011 *) CoefficientList[Series[(x(1-2x))/((1-x)(1-3x)(1-4x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{8, -19, 12}, {0, 1, 6}, 30] (* Harvey P. Dale, Nov 28 2018 *) PROG (MAGMA) [((4^(n+1)-1)/3-3^n)/2: n in [0..30]]; // Vincenzo Librandi, Jul 17 2011 CROSSREFS Sequence in context: A081278 A054146 A172062 * A173413 A008549 A026675 Adjacent sequences:  A081671 A081672 A081673 * A081675 A081676 A081677 KEYWORD easy,nonn AUTHOR Paul Barry, Mar 28 2003 STATUS approved

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Last modified January 16 11:32 EST 2019. Contains 319188 sequences. (Running on oeis4.)