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 A370615 #24 May 03 2024 16:50:44
%S A370615 0,1,2,6,40,1181,755841,286577870992,41063655031092356251961,
%T A370615 843111882268046256673070172994877712169680285,
%U A370615 355418823010783945962646271385485944012152783545060852031848083841154141557381002556807596
%N A370615 a(0) = 0. For n >= 1, a(n) = 1 + (sum of the next consecutive a(n-1) positive integers).
%H A370615 Paolo Xausa, <a href="/A370615/b370615.txt">Table of n, a(n) for n = 0..13</a>
%F A370615 a(0) = 0. For n >= 1, a(n) = A372421(n) - A372421(n-1).
%e A370615 0, 0+1 = 1, 1+1 = 2, 2+3+1 = 6, 4+5+...+9+1 = 40, 10+11+...+49+1 = 1181, ...
%e A370615 | | \_/ \_______/ \__________/
%e A370615 0 terms 1 term 2 terms 6 terms 40 terms
%t A370615 Block[{k = 0}, Differences[NestList[PolygonalNumber[#] + k++ &, 0, 12]]]
%Y A370615 Partial sums give A372421.
%K A370615 nonn
%O A370615 0,3
%A A370615 _Paolo Xausa_, Apr 30 2024