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 A290312 Third diagonal sequence of the Sheffer triangle A094816 (special Charlier). 4

%I

%S 1,8,29,75,160,301,518,834,1275,1870,2651,3653,4914,6475,8380,10676,

%T 13413,16644,20425,24815,29876,35673,42274,49750,58175,67626,78183,

%U 89929,102950,117335,133176,150568,169609,190400,213045,237651,264328,293189,324350,357930

%N Third diagonal sequence of the Sheffer triangle A094816 (special Charlier).

%C See A094816 and A290311.

%H Colin Barker, <a href="/A290312/b290312.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 G.f.: (1 + 3*x - x^2)/(1 - x)^5.

%F E.g.f.: exp(x)*(1 + 7*x + 14*x^2/2! + 11*x^3/3! + 3*x^4/4!). This is computed from the o.g.f. with eqs. (23)-(25) of the _Wolfdieter Lang_ 2017 link in A282629.

%F From _Colin Barker_, Jul 29 2017: (Start)

%F a(n) = (24 + 70*n + 69*n^2 + 26*n^3 + 3*n^4) / 24.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 4.

%F (End)

%o (PARI) Vec((1 + 3*x - x^2)/(1 - x)^5 + O(x^60)) \\ _Colin Barker_, Jul 29 2017

%Y Cf. A094816, A290311.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Jul 28 2017

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Last modified January 27 15:14 EST 2020. Contains 331295 sequences. (Running on oeis4.)