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%I #11 Aug 03 2017 05:49:30
%S 1,24,145,545,1575,3836,8274,16290,29865,51700,85371,135499,207935,
%T 309960,450500,640356,892449,1222080,1647205,2188725,2870791,3721124,
%U 4771350,6057350,7619625,9503676,11760399,14446495,17624895,21365200,25744136,30846024,36763265,43596840,51456825,60462921,70744999,82443660,95710810,110710250
%N Fourth diagonal sequence of the Sheffer triangle A094816 (special Charlier).
%C See A094816 and A290311.
%H Colin Barker, <a href="/A290313/b290313.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F O.g.f: (1 + 17*x - 2*x^2 - x^3)/(1 - x)^7.
%F E.g.f.: exp(x)*(1 + 23*x + 98*x^2/2! + 181*x^3/3! + 170*x^4/4! + 80*x^5/5! + 15*x^6/6!).
%F From _Colin Barker_, Jul 29 2017: (Start)
%F a(n) = (48 + 256*n + 422*n^2 + 303*n^3 + 105*n^4 + 17*n^5 + n^6) / 48.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 6.
%F (End)
%o (PARI) Vec((1 + 17*x - 2*x^2 - x^3) / (1 - x)^7 + O(x^50)) \\ _Colin Barker_, Jul 29 2017
%Y Cf. A094816, A290311, A290312.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Jul 28 2017
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