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 A143866 #14 May 09 2021 10:02:46 %S A143866 1,1,1,2,1,2,3,2,2,5,5,3,4,5,12,7,5,6,10,12,29,11,7,10,15,24,29,69,15, %T A143866 11,14,25,36,58,69,165,22,15,22,35,60,87,138,165,393,937,42,30,44,75, %U A143866 132,203,345,495,786,937,2233,56,42,60,110,180,319,483,825,1179,1874,2233,5322 %N A143866 Eigentriangle of A027293. %C A143866 Left border = partition numbers, A000041 starting (1, 1, 2, 3, 5, 7, ...). Right border = INVERT transform of partition numbers starting (1, 1, 2, 5, 12, ...); with row sums the same sequence but starting (1, 2, 5, 12, ...). Sum of n-th row terms = rightmost term of next row. %C A143866 For another definition of L-eigen-matrix of A027293 see A343234. - _Wolfdieter Lang_, Apr 16 2021 %F A143866 Triangle read by rows, A027293 * (A067687 * 0^(n-k)); 1 <= k <= n. (A067687 * 0^(n-k)) = an infinite lower triangular matrix with the INVERT transform of the partition function as the main diagonal: (1, 1, 2, 5, 12, 29, 69, 165, ...); and the rest zeros. Triangle A027293 = n terms of "partition numbers decrescendo"; by rows = termwise product of n terms of partition decrescendo and n terms of A027293: (1, 1, 2, 5, 12, 29, 69, 165, ...). %e A143866 The triangle begins: %e A143866 n \ k 1 2 3 4 5 6 7 8 9 10 11 ... %e A143866 ------------------------------------------- %e A143866 1: 1 %e A143866 2: 1 1 %e A143866 3: 2 1 2 %e A143866 4: 3 2 2 5 %e A143866 5: 5 3 4 5 12 %e A143866 6: 7 5 6 10 12 29 %e A143866 7: 11 7 10 15 24 29 69 %e A143866 8: 15 11 14 25 36 58 69 165 %e A143866 9: 22 15 22 35 60 87 138 165 393 %e A143866 10: 30 22 30 55 84 145 207 330 393 937 %e A143866 11: 42 30 44 75 132 203 345 495 786 937 2233 %e A143866 ... reformatted and extended by _Wolfdieter Lang_, May 02 2021 %e A143866 Row 4 = (3, 2, 2, 5) = termwise product of (3, 2, 1, 1) and (1, 1, 2, 5) = (3*1, 2*1, 1*2, 1*5). %Y A143866 Cf. A027293, A067687, A000041, A343234. %K A143866 nonn,easy,tabl %O A143866 1,4 %A A143866 _Gary W. Adamson_, Sep 04 2008