A064305 - OEIS

%I #14 Jul 26 2022 10:08:31

%S 1,1430,95235,1338790,9137549,41260086,142648495,409186310,1022586105,

%T 2298558934,4750427771,9170347110,16730290885,29104970870,48618847719,

%U 78419396806,122678791025,186826162710

%N Ninth diagonal of triangle A064094.

%H Vincenzo Librandi, <a href="/A064305/b064305.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).

%F a(n) = 1 + 7*n + 27*n^2 + 75*n^3 + 165*n^4 + 297*n^5 + 429*n^6 + 429*n^7, compare to row n = 7 of Catalan triangle A009766.

%F G.f.: (1 + 1422*x + 83823*x^2 + 616894*x^3 + 1013799*x^4 + 412698*x^5 + 33337*x^6 + 186*x^7)/(1 - x)^8.

%F E.g.f.: exp(x)*(1 + 1429*x + 46188*x^2 + 176229*x^3 + 181170*x^4 + 66792*x^5 + 9438*x^6 + 429*x^7). - _Stefano Spezia_, Jul 24 2022

%t CoefficientList[Series[(1 + 1422 x + 83823 x^2 + 616894 x^3 + 1013799 x^4 + 412698 x^5 + 33337 x^6 + 186 x^7)/(1 - x)^8, {x, 0, 40}], x] (* _Vincenzo Librandi_, Apr 15 2014 *)

%Y Cf. A009766, A064094, A064304 (eighth diagonal).

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Sep 13 2001