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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)