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A349713
Antidiagonal sums of triangle A104684.
4
1, 2, 7, 26, 101, 404, 1645, 6784, 28243, 118442, 499601, 2117366, 9008969, 38458644, 164643197, 706574780, 3038800419, 13093784762, 56513880913, 244283771986, 1057348164103, 4582148496448, 19879232544027, 86331108851932, 375262802895691, 1632570339730086, 7108008200622949
OFFSET
0,2
LINKS
Ömür Deveci and Anthony G. Shannon, Some aspects of Neyman triangles and Delannoy arrays, Mathematica Montisnigri, Volume L, 2021.
FORMULA
a(n) = Sum_{k=0..floor(n/2)} A104684(n-k, k).
G.f.: 1/sqrt(x^4-2*x^2-4*x+1). - Alois P. Heinz, Nov 26 2021
MATHEMATICA
nterms=30; Table[Sum[Binomial[r=n-k, k]Binomial[2r-k, r], {k, 0, Floor[n/2]}], {n, 0, nterms-1}] (* Paolo Xausa, Nov 26 2021 *)
PROG
(PARI) T(n, k) = binomial(n, k)*binomial(2*n-k, n); \\ A104684
a(n) = sum(k=0, n\2, T(n-k, k));
CROSSREFS
Cf. A104684.
Sequence in context: A101850 A279002 A176280 * A045868 A171711 A363293
KEYWORD
nonn
AUTHOR
Michel Marcus, Nov 26 2021
STATUS
approved