The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A328000 a(n) = Sum_{k=0..n}(k!*(n - k)!)/(floor(k/2)!*floor((n - k)/2)!)^2. 3
 1, 2, 5, 16, 28, 96, 160, 512, 896, 2560, 4864, 12288, 25600, 57344, 131072, 262144, 655360, 1179648, 3211264, 5242880, 15466496, 23068672, 73400320, 100663296, 343932928, 436207616, 1593835520, 1879048192, 7314866176, 8053063680, 33285996544, 34359738368 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (0,12,0,-48,0,64). FORMULA a(n) = Sum_{k=0..n} s(k)*s(n-k) where s(n) = A056040(n). a(n) = [x^n] (4*x^2 - x - 1)^2 / (1 - 4*x^2)^3. a(n) = 2^(n - 5)*(n*(n + 2) + 32) if n even else 2^(n - 1)*(n + 1). a(2*n) = A327999(n). a(2*n-1) = A002699(n), (with a(-1) = 0). a(2^n-1) = 2^(2^n - 2 + n) for n >= 1. 2*a(2*n)/2^n = A081908(n+1). 4*a(2*n)/4^n = A145018(n+1). 2*a(2*n-1)/4^n = A001477(n). From Stefano Spezia, Oct 19 2019: (Start) a(n) = n! [x^n] (1/32)*exp(-2*x)*(8 + exp(4*x)*(8 + x)*(3 + 2*x) + x*(13 + 2*x)). a(n) = 12*a(n-2) - 48*a(n-4) + 64*a(n-6) for n > 5. (End) MAPLE swing := n -> n!/iquo(n, 2)!^2: a := n -> add(swing(k)*swing(n-k), k=0..n): seq(`if`(irem(n, 2) = 0, 2 + n*(n + 2)/16, n + 1)*2^(n - 1), n=0..31); MATHEMATICA A32800List[len_] := CoefficientList[Series[(4 x^2 - x - 1)^2 / (1 - 4 x^2)^3 , {x, 0, len}], x]; A32800List[31] PROG (PARI) x='x + O('x^32); Vec(serlaplace(((3*x + 8)*sinh(2*x) + (2*x^2 + 16*(x + 1))*cosh(2*x))/16)) (PARI) Vec((1 + x - 4*x^2)^2 / ((1 - 2*x)^3*(1 + 2*x)^3) + O(x^30)) \\ Colin Barker, Feb 05 2020 (MAGMA) [IsOdd(n) select 2^(n - 1)*(n + 1) else 2^(n - 5)*(n*(n + 2) + 32):n in [0..30]]; // Marius A. Burtea, Feb 05 2020 CROSSREFS Cf. A327999, A328001. Cf. A056040, A002699, A001477, A081908, A145018. Sequence in context: A281980 A137997 A213359 * A323006 A139022 A196025 Adjacent sequences:  A327997 A327998 A327999 * A328001 A328002 A328003 KEYWORD nonn,easy AUTHOR Peter Luschny, Oct 01 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 7 08:12 EDT 2021. Contains 343636 sequences. (Running on oeis4.)