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 A081040 5th binomial transform of (1,4,0,0,0,0,....). 5
 1, 9, 65, 425, 2625, 15625, 90625, 515625, 2890625, 16015625, 87890625, 478515625, 2587890625, 13916015625, 74462890625, 396728515625, 2105712890625, 11138916015625, 58746337890625, 308990478515625, 1621246337890625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..300 Index entries for linear recurrences with constant coefficients, signature (10,-25). FORMULA a(n) = 10*a(n-1)-25*a(n-2), a(0)=1, a(1)=9. a(n) = (4n+5)*5^(n-1). a(n) = sum( k=0..n, (k+1)*4^k Binomial(n, k) ). G.f.: (1-x)/(1-5x)^2. MATHEMATICA CoefficientList[Series[(1 - x) / (1 - 5 x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *) PROG (MAGMA) [(4*n+5)*5^(n-1): n in [0..25]]; // Vincenzo Librandi, Aug 06 2013 (PARI) a(n)=(4*n+5)*5^(n-1) \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Cf. A081039, A081041. Sequence in context: A250415 A237040 A055284 * A102902 A127534 A037548 Adjacent sequences:  A081037 A081038 A081039 * A081041 A081042 A081043 KEYWORD nonn,easy AUTHOR Paul Barry, Mar 03 2003 STATUS approved

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