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%I #11 Feb 08 2022 20:18:27
%S 1,1,3,7,17,40,96,228,544,1296,3089,7361,17544,41810,99643,237471,
%T 565946,1348773,3214424,7660679,18257085,43510652,103695461,247129108,
%U 588963062,1403628615,3345155947,7972242937,18999609718,45280252031
%N Left border of triangle A137680.
%C Each term in the sequence (n > 1) = sum of previous terms of triangle A137680 = partial sums of sequence A137681: (1, 2, 4, 10, 23, ...).
%C Starting (1, 3, 7, ...) = INVERT transform of A160096. - _Gary W. Adamson_, May 01 2009
%F Partial sums of sequence A137681 prefaced with a 1. a(n) is the sum of all terms in rows 1 through (n-1) in triangle A137680.
%e First few rows of triangle A137680 =
%e 1;
%e 1, 1;
%e 3, 0, 1;
%e 7, 2, 0, 1;
%e ...
%e a(5) = 17 is the sum of 1 through 4 row terms of triangle A137680: (1 + 2 + 4 + 10); where (1, 2, 4, 10, 23, ...) = A137681 = row sums of triangle A137680 = first difference row of A137682, n > 1.
%p A137682 := proc(n)
%p A137680(n,1) ;
%p end proc:
%p seq(A137682(n),n=1..30) ; # _R. J. Mathar_, Aug 12 2012
%Y Cf. A137680, A137681.
%Y Cf. A160096.
%K nonn
%O 1,3
%A _Gary W. Adamson_, Feb 05 2008
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