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.
%I A177984 #4 Jul 22 2025 08:10:19
%S A177984 1,1,1,1,4,1,1,14,14,1,1,44,126,44,1,1,132,887,887,132,1,1,390,5451,
%T A177984 12076,5451,390,1,1,1150,30984,131665,131665,30984,1150,1,1,3400,
%U A177984 168076,1252600,2353126,1252600,168076,3400,1,1,10088,885725,10905407,34828859
%N A177984 A symmetrical triangle of polynomial coefficients:p(x,n)=If[n == 0, 1, (1 - x)^(n + 1)*Sum[((2*k + 1)^n + (k + 1)^n + k^n)*x^k, {k, 0, Infinity}]/2].
%C A177984 Row sums are:
%C A177984 {1, 2, 6, 30, 216, 2040, 23760, 327600, 5201280, 93260160, 1861574400,...}.
%F A177984 p(x,n)=If[n == 0, 1, (1 - x)^(n + 1)*Sum[((2*k + 1)^n + (k + 1)^n + k^n)*x^k, {k, 0, Infinity}]/2];
%F A177984 t(n,m)=coefficients(p(x,n))=If[n==0,1,(A008518(n,m)+A060187(n,m))/2]
%e A177984 {1},
%e A177984 {1, 1},
%e A177984 {1, 4, 1},
%e A177984 {1, 14, 14, 1},
%e A177984 {1, 44, 126, 44, 1},
%e A177984 {1, 132, 887, 887, 132, 1},
%e A177984 {1, 390, 5451, 12076, 5451, 390, 1},
%e A177984 {1, 1150, 30984, 131665, 131665, 30984, 1150, 1},
%e A177984 {1, 3400, 168076, 1252600, 2353126, 1252600, 168076, 3400, 1},
%e A177984 {1, 10088, 885725, 10905407, 34828859, 34828859, 10905407, 885725, 10088, 1},
%e A177984 {1, 30026, 4582497, 89401968, 454344414, 764856588, 454344414, 89401968, 4582497, 30026, 1}
%t A177984 p[x_, n_] = If[n == 0, 1, (1 - x)^(n + 1)*Sum[((2* k + 1)^n + (k + 1)^n + k^n)*x^k, {k, 0, Infinity}]/2];
%t A177984 Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];
%t A177984 Flatten[%]
%Y A177984 Cf. A008518, A060187
%K A177984 nonn,tabl,uned
%O A177984 0,5
%A A177984 _Roger L. Bagula_, May 16 2010