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%I #14 Jul 24 2024 09:47:40
%S 1,179,5280,82610,919615,8284857,64730022,457217400,2999230965,
%T 18608607535,110625457964,636103699038,3562753619915,19541111960965,
%U 105392471360850,560747327119908,2950726075955265,15387821226034875,79656442803398680,409857988825489610
%N Fifth column (m=4) of triangle A142963 divided by 16=2^4.
%F a(n) = A142963(n+5,3)/2^4.
%F From _Johannes W. Meijer_, Feb 20 2009: (Start)
%F a(n) = 35a(n-1) - 560a(n-2) + 5432a(n-3) - 35714a(n-4) + 168542a(n-5) - 589632a(n-6) + 1556776a(n-7) - 3126949a(n-8) + 4777591a(n-9) - 5506936a(n-10) + 4703032a(n-11) - 2881136a(n-12) + 1195632a(n-13) - 300672a(n-14) + 34560a(n-15).
%F a(n) = (1155/8) + (472/3)*n - 5544*2^n + (120285/4)*3^n - 49280*4^n + (196875/8)*5^n - 64*2^n*n^3 - 864*2^n*n^2 - 3824*2^n*n + (187/3)*n^2 + 1215*3^n*n^2 + 12150*3^n*n - 8960*4^n*n + (32/3)*n^3 + (2/3)*n^4.
%F G.f.: (1 + 144*z - 425*z^2 - 7382*z^3 + 48451*z^4 - 96764*z^5 - 2559*z^6 + 257002*z^7 - 312444*z^8 + 88344*z^9 + 30240*z^10)/((1-z)^5*(1-2*z)^4*(1-3*z)^3*(1-4*z)^2*(1-5*z)).
%F (End)
%Y Column m=3: 8*A142966.
%Y From _Johannes W. Meijer_, Feb 20 2009: (Start)
%Y Cf. A156925.
%Y Equals A156920(n+4,4).
%Y Equals A156919(n+4,4)/2^n.
%Y (End)
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Sep 15 2008