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.

A112503 Fourth column of triangle A112500.

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%I A112503 #5 Jul 08 2025 17:24:39
%S A112503 1,20,225,1882,13070,79872,444902,2311828,11388999,53820068,246112783,
%T A112503 1096379070,4782801180,20515294320,86808499020,363304109640,
%U A112503 1507010836605,6206407299540,25412183425165,103563957886370
%N A112503 Fourth column of triangle A112500.
%C A112503 For a combinatorial formula see A112500, case k=4.
%H A112503 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (20,-175,882,-2835,6072,-8777,8458,-5204,1848,-288).
%F A112503 G.f.: 1/product((1-j*x)^(5-j), j=1..4) = 1/(((1-x)^4)*((1-2*x)^3)*((1-3*x)^2)*(1-4*x)).
%F A112503 a(n) = 7813/324 + (2251/432)*(n+1) + (31/36)*binomial(n+2, 2) +(1/12)*binomial(n+3, 3) +(-1344 -256*(n+1) - 64*binomial(n+2, 2))*2^n + (6561/4 - (6561/16)*(n+1))*3^n + (32768/81)*4^n, n>=0 (from partial fractions for g.f.).
%K A112503 nonn,easy
%O A112503 0,2
%A A112503 _Wolfdieter Lang_, Oct 14 2005