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 A081908 a(n) = 2^n*(n^2 - n + 8)/8. 5
 1, 2, 5, 14, 40, 112, 304, 800, 2048, 5120, 12544, 30208, 71680, 167936, 389120, 892928, 2031616, 4587520, 10289152, 22937600, 50855936, 112197632, 246415360, 538968064, 1174405120, 2550136832, 5519704064, 11911823360, 25635586048 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A000124 (when this begins 1,1,2,4,7,...). 2nd binomial transform of (1,0,1,0,0,0,...). Case k=2 where a(n,k) = k^n(n^2 - n + 2k^2)/(2k^2) with g.f. (1 - 2kx + (k^2+1)x^2)/(1-kx)^3. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..200 from Vincenzo Librandi) Index entries for linear recurrences with constant coefficients, signature (6,-12,8). FORMULA G.f.: (1 - 4*x + 5*x^2)/(1-2*x)^3. a(n) = A000079(n) + (A001788(n) - A001787(n))/2. - Paul Barry, May 27 2003 a(n) = Sum_{k=0..n} C(n, k)*(1 + C(k, 2)). - Paul Barry, May 27 2003 E.g.f.: (2 + x^2)*exp(2*x)/2. - G. C. Greubel, Oct 17 2018 MATHEMATICA Table[2^n*(n^2-n+8)/8, {n, 0, 50}] (* or *) LinearRecurrence[{6, -12, 8}, {1, 2, 5}, 50] (* G. C. Greubel, Oct 17 2018 *) PROG (MAGMA) [2^n*(n^2-n+8)/8: n in [0..40]]; Vincenzo Librandi, Apr 27 2011 (PARI) a(n)=2^n*(n^2-n+8)/8 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Cf. A081909. Sequence in context: A111110 A296516 A111109 * A221677 A229737 A059505 Adjacent sequences:  A081905 A081906 A081907 * A081909 A081910 A081911 KEYWORD easy,nonn,changed AUTHOR Paul Barry, Mar 31 2003 STATUS approved

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Last modified October 18 18:10 EDT 2018. Contains 316323 sequences. (Running on oeis4.)