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A064338 Row sums of signed triangle A064334. 3
1, 2, 3, 3, 3, 4, -6, 49, -178, 76, 8633, -124131, 1202662, -8252662, 16009623, 730544913, -17236420029, 256679586178, -2787185606474, 15947981601793, 215110909342463, -9723413157539188, 216257810122284716, -3515999949642686709 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = 1 + Sum_{0<=k<=n-1} hypergeom([1-n+k,n-k],[-n+k],-k). - Robert Israel, Jan 03 2019
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 *)
CROSSREFS
Cf. A064339 (row sums of unsigned triangle A064334).
Sequence in context: A035581 A171628 A205566 * A197592 A103359 A020481
KEYWORD
sign
AUTHOR
Wolfdieter Lang, Sep 21 2001
STATUS
approved

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Last modified June 18 23:53 EDT 2024. Contains 373490 sequences. (Running on oeis4.)