A067352 - OEIS

A067352

Divide the natural numbers in sets of consecutive numbers starting with {1,2} as the first set. The number of elements of the n-th set is equal to the sum of the n-1 final numbers in the (n-1)st set. The number of elements of the n-th set gives a(n).

2, 2, 7, 30, 158, 985, 7089, 57890, 529276, 5358915, 59543495, 720476284, 9431689530, 132829627541, 2002662076765, 32185640519430, 549301598198264, 9921760117456135, 189097075179752211, 3792446896660586000, 79840987298117599990, 1760493769923493079769, 40575189744903364314665

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..23.

FORMULA

a(n) = (1+a(1)+a(2)+...+a(n-1)-n/2)*(n-1).

EXAMPLE

The sets begin {1,2},{3,4},{5,6,...,9,10,11},{12,13,...,38,39,40,41},...

PROG

(PARI) a(n) = if (n==1, 2, (1+sum(k=1, (n-1), a(k)) - n/2)*(n-1)); \\ Michel Marcus, Sep 10 2017

CROSSREFS