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a(0) = 0. For n >= 1, a(n) = 1 + (sum of the next consecutive a(n-1) positive integers).
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%I #24 May 03 2024 16:50:44

%S 0,1,2,6,40,1181,755841,286577870992,41063655031092356251961,

%T 843111882268046256673070172994877712169680285,

%U 355418823010783945962646271385485944012152783545060852031848083841154141557381002556807596

%N a(0) = 0. For n >= 1, a(n) = 1 + (sum of the next consecutive a(n-1) positive integers).

%H Paolo Xausa, <a href="/A370615/b370615.txt">Table of n, a(n) for n = 0..13</a>

%F a(0) = 0. For n >= 1, a(n) = A372421(n) - A372421(n-1).

%e 0, 0+1 = 1, 1+1 = 2, 2+3+1 = 6, 4+5+...+9+1 = 40, 10+11+...+49+1 = 1181, ...

%e | | \_/ \_______/ \__________/

%e 0 terms 1 term 2 terms 6 terms 40 terms

%t Block[{k = 0}, Differences[NestList[PolygonalNumber[#] + k++ &, 0, 12]]]

%Y Partial sums give A372421.

%K nonn

%O 0,3

%A _Paolo Xausa_, Apr 30 2024