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%I #15 Dec 12 2015 13:12:55
%S 1,140,11550,735000,39991875,1960612500,89303500000,3853850000000,
%T 159664583203125,6409926960937500,251055710800781250,
%U 9641722822265625000,364483553427490234375,13602971247133789062500,502386213470141601562500,18394848021467285156250000
%N Seventh column of triangle A075500.
%C The e.g.f. given below is Sum_{m=0..6}(A075513(7,m)exp(5*(m+1)*x))/6!.
%H Colin Barker, <a href="/A075915/b075915.txt">Table of n, a(n) for n = 0..646</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (140,-8050,245000,-4230625,41037500,-204187500,393750000).
%F a(n) = A075500(n+7, 7) = (5^n)S2(n+7, 7) with S2(n, m) = A008277(n, m) (Stirling2).
%F a(n) = Sum_{m=0..6}(A075513(7, m)*(5*(m+1))^n)/6!.
%F G.f.: 1/Product_{k=1..7}(1-5k*x).
%F E.g.f.: (d^7/dx^7)((((exp(5x)-1)/5)^7)/7!) = (exp(5*x) - 384*exp(10*x) + 10935*exp(15*x) - 81920*exp(20*x) + 234375*exp(25*x) - 279936*exp(30*x) + 117649*exp(35*x))/6!.
%F G.f.: 1 / ((1-5*x)*(1-10*x)*(1-15*x)*(1-20*x)*(1-25*x)*(1-30*x)*(1-35*x)). - _Colin Barker_, Dec 12 2015
%t Table[5^(n-1) * (1 - 3*2^(7 + n) - 5*2^(14 + 2*n) + 5*3^(7 + n) + 3*5^(7 + n) - 6^(7 + n) + 7^(6 + n))/144, {n, 0, 20}] (* _Vaclav Kotesovec_, Dec 12 2015 *)
%o (PARI) Vec(1/((1-5*x)*(1-10*x)*(1-15*x)*(1-20*x)*(1-25*x)*(1-30*x)*(1-35*x)) + O(x^30)) \\ _Colin Barker_, Dec 12 2015
%Y Cf. A000351, A016164, A075911, A075912, A075913, A075914.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Oct 02 2002
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