A064338 - OEIS

%I #13 Feb 06 2023 07:56:50

%S 1,2,3,3,3,4,-6,49,-178,76,8633,-124131,1202662,-8252662,16009623,

%T 730544913,-17236420029,256679586178,-2787185606474,15947981601793,

%U 215110909342463,-9723413157539188,216257810122284716,-3515999949642686709

%N Row sums of signed triangle A064334.

%H Robert Israel, <a href="/A064338/b064338.txt">Table of n, a(n) for n = 0..488</a>

%F a(n) = 1 + Sum_{0<=k<=n-1} hypergeom([1-n+k,n-k],[-n+k],-k). - _Robert Israel_, Jan 03 2019

%p f:= proc(n) local k; 1 + add(simplify(hypergeom([1-n+k,n-k],[-n+k],-k)),k=0..n-1) end proc:

%p map(f, [$0..50]); # _Robert Israel_, Jan 03 2019

%t a[n_] := If[n == 0, 1, Sum[(n-k-j)*Binomial[n-k-1+j, j]* (-k)^j/(n-k), {k, 1, n-1}, {j, 0, n-k-1}] + 2];

%t Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Feb 06 2023 *)

%Y Cf. A064339 (row sums of unsigned triangle A064334).

%K sign

%O 0,2

%A _Wolfdieter Lang_, Sep 21 2001