cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A075910 Seventh column of triangle A075499.

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%I A075910 #10 Aug 11 2021 12:58:12
%S A075910 1,112,7392,376320,16380672,642453504,23410376704,808210923520,
%T A075910 26787271999488,860325833342976,26956901684084736,828217683974553600,
%U A075910 25047119070415028224,747831252926309859328,22095179333791056396288
%N A075910 Seventh column of triangle A075499.
%C A075910 The e.g.f. given below is Sum_{m=0..6} A075513(7,m)*exp(4*(m+1)*x)/6!.
%F A075910 a(n) = A075499(n+7, 7) = (4^n)*S2(n+7, 7) with S2(n, m) := A008277(n, m) (Stirling2).
%F A075910 a(n) = Sum_{m=0..6} A075513(7, m)*((m+1)*4)^n/6!.
%F A075910 G.f.: 1/Product_{k=1..7} (1 - 4*k*x).
%F A075910 E.g.f.: (d^7/dx^7)(((exp(4*x)-1)/4)^7)/7! = (exp(4*x) - 384*exp(8*x) + 10935*exp(12*x) - 81920*exp(16*x) + 234375*exp(20*x) - 279936*exp(24*x) + 117649*exp(28*x))/6!.
%t A075910 CoefficientList[Series[1/Product[1-4k x,{k,7}],{x,0,20}],x] (* _Harvey P. Dale_, Aug 11 2021 *)
%Y A075910 Cf. A075509.
%K A075910 nonn,easy
%O A075910 0,2
%A A075910 _Wolfdieter Lang_, Oct 02 2002