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 A144061 #5 Jun 02 2025 00:33:47
%S A144061 1,1,1,1,3,2,1,5,10,6,1,7,22,42,22,1,9,38,114,198,94,1,11,58,234,638,
%T A144061 1034,454,1,13,82,414,1518,3854,5902,2430,1,15,110,666,3058,10434,
%U A144061 24970,36450,14214,1,17,142,1002,5522,23594,75818,172530,241638,89918
%N A144061 Eigentriangle generated from A109128, row sums = expansion of {2(exp(x)-1)}.
%C A144061 Row sums = A001861: (1, 2, 6, 22, 94, 454, 2430,...) = expansion of {2(exp(x)-1)}
%C A144061 Right border = A001861 shifted: (1, 1, 2, 6, 22, 94,...).
%C A144061 Sum of n-th row terms = rightmost term of next row.
%F A144061 T(n,k) = A109128(n,k)*A001861(k-1).
%F A144061 A109128 = (2*binomial(n,k) - 1): (1; 1,1; 1,3,1; 1,5,5,1;...).
%F A144061 A001861(k-1) = A001861 shifted one place, = (1, 1, 2, 6, 22, 94, 454,...).
%e A144061 First few rows of the triangle =
%e A144061 1;
%e A144061 1, 1;
%e A144061 1, 3, 2;
%e A144061 1, 5, 10, 6;
%e A144061 1, 7, 22, 42, 22;
%e A144061 1, 9, 38, 114, 198, 94;
%e A144061 1, 11, 58, 234, 638, 1034, 454;
%e A144061 1, 13, 82, 414, 1518, 3854, 5902, 2430;
%e A144061 1, 15, 110, 666, 3058, 10434, 24970, 36450, 14214;
%e A144061 ...
%e A144061 Example: row 3 = (1, 5, 10, 6) = termwise products of (1, 5, 5, 1) and (1, 1, 2, 6), where (1, 5, 5, 1) = row 3 of triangle A109128 and (1, 1, 2, 6) = the first 4 terms of A001861 shifted.
%Y A144061 A109128, Cf. A001861
%K A144061 nonn,tabl
%O A144061 1,5
%A A144061 _Gary W. Adamson_ & _Roger L. Bagula_, Sep 09 2008