A178833 Partial sums of "Half-Catalan numbers" A000992.

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

Author

Jonathan Vos Post, Jan 01 2011

Keywords

• nonn
• easy

Comments

The subsequence of primes begins: 2, 3, 5, 199, 4261, 493184761.

The subsequence of perfect powers begins: 1, 8, 25, 49.

Examples

			A000992 starts with 1, 1, 1, 2, 3, ... giving partial sums 1, 2, 3, 5, 8 ...
		

Crossrefs

Cf. A000992, A001190, A093637, A124973.

Programs

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

PARI

lista(nn) = for (k=1, nn, print1(vecsum(A000992_list(k)), ", ")); \\ Michel Marcus, Feb 16 2015

Formula

a(n) = Sum_{i=1..n} A000992(i).