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 A126958 Define an array by d(m, 0) = 1, d(m, 1) = m; d(m, k) = (m - k + 1) d(m+1, k-1) - (k-1) (m+1) d(m+2, k-2). Sequence gives d(n,4). 2

%I #9 Oct 21 2022 21:13:53

%S 36,24,-60,-216,-420,-624,-756,-720,-396,360,1716,3864,7020,11424,

%T 17340,25056,34884,47160,62244,80520,102396,128304,158700,194064,

%U 234900,281736,335124,395640,463884,540480,626076,721344,826980,943704,1072260,1213416,1367964

%N Define an array by d(m, 0) = 1, d(m, 1) = m; d(m, k) = (m - k + 1) d(m+1, k-1) - (k-1) (m+1) d(m+2, k-2). Sequence gives d(n,4).

%D V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.

%H G. C. Greubel, <a href="/A126958/b126958.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F a(n) = (n+3)*(n+1)*(n^2 -10*n +12).

%F From _G. C. Greubel_, Jan 29 2020: (Start)

%F G.f.: 12*(3 -13*x +15*x^2 -3*x^3)/(1-x)^5.

%F E.g.f.: (36 -12*x -36*x^2 +x^4)*exp(x). (End)

%p seq( (n+3)*(n+1)*(n^2 -10*n +12), n=0..40); # _G. C. Greubel_, Jan 29 2020

%t Table[(n+3)*(n+1)*(n^2 -10*n +12), {n,0,40}] (* _G. C. Greubel_, Jan 29 2020 *)

%o (PARI) vector(41, n, my(m=n-1); (m+3)*(m+1)*(m^2 -10*m +12)) \\ _G. C. Greubel_, Jan 29 2020

%o (Magma) [(n+3)*(n+1)*(n^2 -10*n +12): n in [0..40]]; // _G. C. Greubel_, Jan 29 2020

%o (Sage) [(n+3)*(n+1)*(n^2 -10*n +12) for n in (0..40)] # _G. C. Greubel_, Jan 29 2020

%o (GAP) List([0..40], n-> (n+3)*(n+1)*(n^2 -10*n +12)); # _G. C. Greubel_, Jan 29 2020

%Y A row of A105937.

%K sign,easy

%O 0,1

%A Vincent v.d. Noort, Mar 21 2007

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Last modified September 28 13:02 EDT 2023. Contains 365735 sequences. (Running on oeis4.)