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 A178833 #29 Nov 04 2024 11:17:23
%S A178833 1,2,3,5,8,14,25,49,96,199,413,894,1924,4261,9392,21205,47534,108492,
%T A178833 246313,568003,1302431,3024429,6990985,16343338,38026783,89322813,
%U A178833 208986625,493184761,1159317065,2745547588,6480141829,15399987104,36475269692,86916706534,206503331542
%N A178833 Partial sums of "Half-Catalan numbers" A000992.
%C A178833 The subsequence of primes begins: 2, 3, 5, 199, 4261, 493184761.
%C A178833 The subsequence of perfect powers begins: 1, 8, 25, 49.
%F A178833 a(n) = Sum_{i=1..n} A000992(i).
%e A178833 A000992 starts with 1, 1, 1, 2, 3, ... giving partial sums 1, 2, 3, 5, 8 ...
%p A178833 b:= proc(n) option remember; `if`(n=1, 1,
%p A178833 add(b(j)*b(n-j), j=1..n/2))
%p A178833 end:
%p A178833 a:= proc(n) option remember; `if`(n<1, 0, b(n)+a(n-1)) end:
%p A178833 seq(a(n), n=1..42); # _Alois P. Heinz_, Nov 04 2024
%o A178833 (PARI) lista(nn) = for (k=1, nn, print1(vecsum(A000992_list(k)), ", ")); \\ _Michel Marcus_, Feb 16 2015
%Y A178833 Cf. A000992, A001190, A093637, A124973.
%K A178833 nonn,easy
%O A178833 1,2
%A A178833 _Jonathan Vos Post_, Jan 01 2011