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 A077385 #13 Sep 21 2022 03:20:19
%S A077385 1,1,2,1,1,3,9,3,1,1,4,16,64,16,4,1,1,5,25,125,625,125,25,5,1,1,6,36,
%T A077385 216,1296,7776,1296,216,36,6,1,1,7,49,343,2401,16807,117649,16807,
%U A077385 2401,343,49,7,1,1,8,64,512,4096,32768,262144,2097152,262144,32768,4096,512,64,8,1
%N A077385 Triangle read by rows in which n-th row contains 2n-1 terms starting from n^0 to n^(n-1) in increasing order and then in decreasing order to n^0.
%H A077385 G. C. Greubel, <a href="/A077385/b077385.txt">Rows n = 1..40 of the irregular triangle, flattened</a>
%F A077385 T(n, k) = n^k for k < n, otherwise n^(2*n-k-2), for n >= 1, 0 <= k <= 2*n-2.
%F A077385 From _G. C. Greubel_, Sep 21 2022: (Start)
%F A077385 T(n, 0) = T(n, 2*n-2) = 1.
%F A077385 T(n, n-1) = A000169(n).
%F A077385 T(n, n) = A000272(n).
%F A077385 T(n, 2*n-2-k) = T(n, k).
%F A077385 Sum_{k=0..n-1} T(n, k) = A023037(n).
%F A077385 Sum_{k=0..n-2} T(n, k) = A060072(n).
%F A077385 Sum_{k=0..2*n-2} T(n, k) = A077386(n) = 2*A060072(n) + A000169(n), n > 1. (End)
%e A077385 Irregular triangle begins as:
%e A077385 1;
%e A077385 1, 2, 1;
%e A077385 1, 3, 9, 3, 1;
%e A077385 1, 4, 16, 64, 16, 4, 1;
%e A077385 1, 5, 25, 125, 625, 125, 25, 5, 1;
%e A077385 1, 6, 36, 216, 1296, 7776, 1296, 216, 36, 6, 1;
%e A077385 1, 7, 49, 343, 2401, 16807, 117649, 16807, 2401, 343, 49, 7, 1;
%p A077385 A077385 := proc(n,k) if k < n then n^k ; else n^(2*n-k-2) ; fi ; end: for n from 1 to 10 do for k from 0 to 2*n-2 do printf("%d, ",A077385(n,k)) ; od : od : # _R. J. Mathar_, Jul 03 2007
%t A077385 Table[Join[n^Range[0,n-1],n^Range[n-2,0,-1]],{n,8}]//Flatten (* _Harvey P. Dale_, Oct 13 2017 *)
%o A077385 (Magma)
%o A077385 A077385:= func< n,k | k lt n select n^k else n^(2*n-k-2) >;
%o A077385 [A077385(n,k): k in [0..2*n-2], n in [1..12]]; // _G. C. Greubel_, Sep 21 2022
%o A077385 (SageMath)
%o A077385 def A077385(n,k): return n^k if (k<n) else n^(2*n-k-2)
%o A077385 flatten([[A077385(n,k) for k in (0..2*n-2)] for n in (1..12)]) # _G. C. Greubel_, Sep 21 2022
%Y A077385 Cf. A000169, A000272, A023037, A060072, A077386.
%K A077385 nonn,tabf
%O A077385 1,3
%A A077385 _Amarnath Murthy_, Nov 06 2002
%E A077385 More terms from _R. J. Mathar_, Jul 03 2007