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 A081042 7th binomial transform of (1,6,0,0,0,0,0,0,...). 3
 1, 13, 133, 1225, 10633, 88837, 722701, 5764801, 45294865, 351652861, 2703691669, 20620693177, 156208812697, 1176509412085, 8816899947037, 65787638066353, 488998835524129, 3622389432086509, 26752509108528805, 197038045347164329 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..300 Silvana Ramaj, New Results on Cyclic Compositions and Multicompositions, Master's Thesis, Georgia Southern Univ., 2021. See p. 67. Index entries for linear recurrences with constant coefficients, signature (14,-49). FORMULA a(n) = 14*a(n-1) - 49*a(n-2) for n>1, a(0)=1, a(1)=13. a(n) = (6*n+7)*7^(n-1). a(n) = Sum_{k=0..n} (k+1)*6^k*binomial(n, k). G.f.: (1-x)/(1-7*x)^2. MATHEMATICA CoefficientList[Series[(1 - x)/(1 - 7 x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *) LinearRecurrence[{14, -49}, {1, 13}, 20] (* Harvey P. Dale, Jan 24 2014 *) PROG (Magma) [(6*n+7)*7^(n-1): n in [0..25]]; // Vincenzo Librandi, Aug 06 2013 CROSSREFS Cf. A081041, A081042. Sequence in context: A199144 A198664 A332243 * A329019 A016153 A187732 Adjacent sequences: A081039 A081040 A081041 * A081043 A081044 A081045 KEYWORD nonn,easy AUTHOR Paul Barry, Mar 04 2003 STATUS approved

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Last modified May 30 03:30 EDT 2024. Contains 372957 sequences. (Running on oeis4.)