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

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.

Links

Table of n, a(n) for n=1..32.

Formula

a(n) = SUM[i=1..n] A000992(i).

a(n) = SUM[i=1..n] SUM[k=1..floor(i/2)] a(k)*a(i-k), with a(1) = 1.

Example

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

Prog

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

Crossrefs

Cf. A000992, A001190, A093637, A124973.

Sequence in context: A177510 A062178 A173282 * A212657 A065955 A196118

Adjacent sequences: A178830 A178831 A178832 * A178834 A178835 A178836

Keyword

nonn,easy

Author

Jonathan Vos Post, Jan 01 2011

Status

approved