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%I A290314 #10 Aug 03 2017 05:49:24
%S A290314 1,89,814,4179,15659,47775,125853,296703,641058,1290718,2451449,
%T A290314 4432792,7686042,12851762,20818302,32792898,50387031,75717831,
%U A290314 111527416,161322161,229533997,321705945,444704195,606959145,818737920,1092450996,1442995659,1888139134,2448944324,3150241204,4021147020,5095638548
%N A290314 Fifth diagonal sequence of the Sheffer triangle A094816 (special Charlier).
%C A290314 See A094816 and A290311.
%H A290314 Colin Barker, <a href="/A290314/b290314.txt">Table of n, a(n) for n = 0..1000</a>
%H A290314 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A290314 O.g.f.: (1  + 80*x + 49*x^2 - 27*x^3 + 2*x^4)/(1-x)^9.
%F A290314 E.g.f: exp(x)*(1 + 88*x + 637*x^2/2! + 2003*x^3/3! + 3472*x^4/4! + 3574*x^5/5! + 2185*x^6/6! + 735*x^7/7! + 105*x^8/8!).
%F A290314 From _Colin Barker_, Jul 29 2017: (Start)
%F A290314 a(n) = (5760 + 67248*n + 158180*n^2 + 161700*n^3 + 87695*n^4 + 26952*n^5 + 4670*n^6 + 420*n^7 + 15*n^8) / 5760.
%F A290314 a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>8.
%F A290314 (End)
%o A290314 (PARI) Vec((1 + 80*x + 49*x^2 - 27*x^3 + 2*x^4) / (1 - x)^9 + O(x^50)) \\ _Colin Barker_, Jul 29 2017
%Y A290314 Cf. A094816, A290311, A290312, A290313.
%K A290314 nonn,easy
%O A290314 0,2
%A A290314 _Wolfdieter Lang_, Jul 28 2017

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