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A178833
Partial sums of "Half-Catalan numbers" A000992.
0
1, 2, 3, 5, 8, 14, 25, 49, 96, 199, 413, 894, 1924, 4261, 9392, 21205, 47534, 108492, 246313, 568003, 1302431, 3024429, 6990985, 16343338, 38026783, 89322813, 208986625, 493184761, 1159317065, 2745547588, 6480141829, 15399987104, 36475269692, 86916706534, 206503331542
OFFSET
1,2
COMMENTS
The subsequence of primes begins: 2, 3, 5, 199, 4261, 493184761.
The subsequence of perfect powers begins: 1, 8, 25, 49.
FORMULA
a(n) = Sum_{i=1..n} A000992(i).
EXAMPLE
A000992 starts with 1, 1, 1, 2, 3, ... giving partial sums 1, 2, 3, 5, 8 ...
MAPLE
b:= proc(n) option remember; `if`(n=1, 1,
add(b(j)*b(n-j), j=1..n/2))
end:
a:= proc(n) option remember; `if`(n<1, 0, b(n)+a(n-1)) end:
seq(a(n), n=1..42); # Alois P. Heinz, Nov 04 2024
PROG
(PARI) lista(nn) = for (k=1, nn, print1(vecsum(A000992_list(k)), ", ")); \\ Michel Marcus, Feb 16 2015
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Jonathan Vos Post, Jan 01 2011
STATUS
approved