OFFSET
1,3
LINKS
Peter Luschny, Row(n) for n = 1..25
Dominique Foata and Guo-Niu Han, Seidel Triangle Sequences and Bi-Entringer Numbers, November 20, 2013.
Foata, Dominique; Han, Guo-Niu; Strehl, Volker The Entringer-Poupard matrix sequence. Linear Algebra Appl. 512, 71-96 (2017).
Christiane Poupard, Deux propriétés des arbres binaires ordonnés stricts, Europ. J. Combin., vol. 10, 1989, p. 369-374.
FORMULA
4^(-n)*sum(k=1..2*n+1, binomial(2*n,k-1)*T(n+1,k)) = A000364(n), n>=0. - Peter Luschny, May 11 2014
(-1)^n*sum(k=1..2*n+1, (-1)^(k-1)*binomial(2*n,k-1)*T(n+1,k)) = A000302(n), n>=0. - Peter Luschny, May 11 2014
EXAMPLE
Triangle begins:
1,
0, 2, 0,
0, 4, 8, 4, 0,
0, 32, 64, 80, 64, 32, 0,
0, 544, 1088, 1504, 1664, 1504, 1088, 544, 0,
...
MAPLE
T := proc(n, k) option remember; local j;
if n = 1 then 1
elif k = 1 then 0
elif k = 2 then 2*add(T(n-1, j), j=1..2*n-3)
elif k > n then T(n, 2*n-k)
else 2*T(n, k-1)-T(n, k-2)-4*T(n-1, k-2)
fi end:
seq(print(seq(T(n, k), k=1..2*n-1)), n=1..6); # Peter Luschny, May 11 2014
MATHEMATICA
T[n_, k_] /; 1 <= k <= 2n-1 := T[n, k] = Which[n == 1, 1, k == 1, 0, k == 2, 2 Sum[T[n-1, j], {j, 1, 2n-3}], k > n, T[n, 2n-k], True, 2 T[n, k-1] - T[n, k-2] - 4 T[n-1, k-2]]; T[_, _] = 0;
Table[T[n, k], {n, 1, 7}, {k, 1, 2n-1}] // Flatten (* Jean-François Alcover, Jul 08 2019, from Maple *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Feb 17 2014
EXTENSIONS
More terms from Peter Luschny, May 11 2014
STATUS
approved