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 A176027 Binomial transform of A005563. 5
 0, 3, 14, 48, 144, 400, 1056, 2688, 6656, 16128, 38400, 90112, 208896, 479232, 1089536, 2457600, 5505024, 12255232, 27131904, 59768832, 131072000, 286261248, 622854144, 1350565888, 2919235584, 6291456000, 13522436096 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The numbers appear on the diagonal of a table T(n,k), where the left column contains the elements of A005563, and further columns are recursively T(n,k) = T(n,k-1)+T(n-1,k-1): ....0....-1.....0.....0.....0.....0.....0.....0.....0.....0. ....3.....3.....2.....2.....2.....2.....2.....2.....2.....2. ....8....11....14....16....18....20....22....24....26....28. ...15....23....34....48....64....82...102...124...148...174. ...24....39....62....96...144...208...290...392...516...664. ...35....59....98...160...256...400...608...898..1290..1806. ...48....83...142...240...400...656..1056..1664..2562..3852. ...63...111...194...336...576...976..1632..2688..4352..6914. ...80...143...254...448...784..1360..2336..3968..6656.11008. ...99...179...322...576..1024..1808..3168..5504..9472.16128. ..120...219...398...720..1296..2320..4128..7296.12800.22272. The second column is A142463, the third A060626, the fourth essentially A035008 and the fifth essentially A016802. Transposing the array gives A005563 and its higher order differences in the individual rows. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..3000 Index entries for linear recurrences with constant coefficients, signature (6,-12,8). FORMULA G.f.: x*(-3+4*x)/(2*x-1)^3. - R. J. Mathar, Dec 11 2010 a(n) = 2^(n-2)*n*(5+n). - R. J. Mathar, Dec 11 2010 a(n) = A127276(n) - A127276(n+1). a(n+1)-a(n) = A084266(n+1). a(n+2) = 16*A058396(n) for n > 0. a(n) = 2*a(n-1) + A001792(n). a(n) = A001793(n) - 2^(n-1) for n > 0. - Brad Clardy, Mar 02 2012 a(n) = Sum_{k=0..n-1} Sum_{i=0..n-1} (k+3) * C(n-1,i). - Wesley Ivan Hurt, Sep 20 2017 From Amiram Eldar, Aug 13 2022: (Start) Sum_{n>=1} 1/a(n) = 1322/75 - 124*log(2)/5. Sum_{n>=1} (-1)^(n+1)/a(n) = 132*log(3/2)/5 - 782/75. (End) MATHEMATICA LinearRecurrence[{6, -12, 8}, {0, 3, 14}, 30] (* Harvey P. Dale, Oct 19 2015 *) PROG (Magma) [2^(n-2)*n*(5+n) : n in [0..30]]; // Vincenzo Librandi, Oct 08 2011 (PARI) a(n)=n*(n+5)<<(n-2) \\ Charles R Greathouse IV, Sep 21 2017 CROSSREFS Cf. A001792, A001793, A005563, A058396, A084266, A127276. Sequence in context: A006900 A212505 A024453 * A345690 A139263 A354507 Adjacent sequences: A176024 A176025 A176026 * A176028 A176029 A176030 KEYWORD nonn,easy AUTHOR Paul Curtz, Dec 06 2010 STATUS approved

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Last modified November 29 13:08 EST 2023. Contains 367445 sequences. (Running on oeis4.)