A064338 Row sums of signed triangle A064334.

1, 2, 3, 3, 3, 4, -6, 49, -178, 76, 8633, -124131, 1202662, -8252662, 16009623, 730544913, -17236420029, 256679586178, -2787185606474, 15947981601793, 215110909342463, -9723413157539188, 216257810122284716, -3515999949642686709

Offset: 0

Author

Wolfdieter Lang, Sep 21 2001

Keywords

• sign

Links

• Robert Israel, Table of n, a(n) for n = 0..488

Crossrefs

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

Programs

Maple

f:= proc(n) local k; 1 + add(simplify(hypergeom([1-n+k,n-k],[-n+k],-k)),k=0..n-1) end proc:
map(f, [$0..50]); # Robert Israel, Jan 03 2019

Mathematica

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];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Feb 06 2023 *)

Formula

a(n) = 1 + Sum_{0<=k<=n-1} hypergeom([1-n+k,n-k],[-n+k],-k). - Robert Israel, Jan 03 2019