A112497 - OEIS

%I #11 Nov 14 2017 03:04:29

%S 105,2205,26775,247555,1939630,13609310,88346258,541831290,3184396215,

%T 18114492851,100467071393,546227989621,2923225973476,15447710150460,

%U 80807432442660,419245751359380,2160664798858005,11075023230179865

%N Fifth column of triangle A112493 used for e.g.f.s of Stirling2 diagonals.

%H G. C. Greubel, <a href="/A112497/b112497.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (35, -560, 5432, -35714, 168542, -589632, 1556776, -3126949, 4777591, -5506936, 4703032, -2881136, 1195632, -300672, 34560).

%F G.f.: (105-1470*x+8400*x^2-25130*x^3+41615*x^4-36280*x^5+13048*x^6) / product((1-j*x)^(6-j), j=1..5).

%F a(n) = 5*a(n-1) + (n+7)*A112496(n).

%t CoefficientList[Series[(105 - 1470*x + 8400*x^2 - 25130*x^3 + 41615*x^4 - 36280*x^5 + 13048*x^6)/Product[(1 - j*x)^(6 - j), {j, 1, 5}], {x, 0, 50}], x] (* _G. C. Greubel_, Nov 13 2017 *)

%o (PARI) x='x+O('x^50); Vec((105 -1470*x +8400*x^2 -25130*x^3 +41615*x^4 -36280*x^5 +13048*x^6)/((1-x)^5*(1-2*x)^4*(1-3*x)^3*(1-4*x)^2*(1-5*x))) \\ _G. C. Greubel_, Nov 13 2017

%Y Cf. A112496 (fourth column).

%Y Column k=4 of A124324 (shifted).

%K nonn,easy

%O 0,1

%A _Wolfdieter Lang_, Oct 14 2005