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A330608
T(n, k) = P(n-k, k) where P(n, x) = Sum_{k=0..n} A053121(n, k)*x^k. Triangle read by rows, for 0 <= k <= n.
0
1, 0, 1, 1, 1, 1, 0, 2, 2, 1, 2, 3, 5, 3, 1, 0, 6, 12, 10, 4, 1, 5, 10, 30, 33, 7, 5, 1, 0, 20, 74, 110, 72, 26, 6, 1, 14, 35, 185, 366, 306, 135, 37, 7, 1, 0, 70, 460, 1220, 1300, 702, 228, 50, 8, 1, 42, 126, 1150, 4065, 5525, 3650, 1406, 357, 65, 9, 1
OFFSET
0,8
EXAMPLE
Triangle starts:
[0] [ 1]
[1] [ 0, 1]
[2] [ 1, 1, 1]
[3] [ 0, 2, 2, 1]
[4] [ 2, 3, 5, 3, 1]
[5] [ 0, 6, 12, 10, 4, 1]
[6] [ 5, 10, 30, 33, 17, 5, 1]
[7] [ 0, 20, 74, 110, 72, 26, 6, 1]
[8] [14, 35, 185, 366, 306, 135, 37, 7, 1]
[9] [ 0, 70, 460, 1220, 1300, 702, 228, 50, 8, 1]
MAPLE
A053121 := (n, k, x) -> irem(n+k+1, 2)*x^k*(k+1)*binomial(n+1, (n-k)/2)/(n+1):
P := (n, x) -> add(A053121(n, k, x), k=0..n):
seq(seq(P(n-k, k), k=0..n), n=0..10);
CROSSREFS
Cf. A053121.
Sequence in context: A239481 A200114 A120652 * A113825 A011138 A022479
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Jan 01 2020
STATUS
approved