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A344563
T(n, k) = binomial(n - 1, k - 1) * binomial(n, k) * 2^k, T(0, 0) = 1. Triangle read by rows, T(n, k) for 0 <= k <= n.
0
1, 0, 2, 0, 4, 4, 0, 6, 24, 8, 0, 8, 72, 96, 16, 0, 10, 160, 480, 320, 32, 0, 12, 300, 1600, 2400, 960, 64, 0, 14, 504, 4200, 11200, 10080, 2688, 128, 0, 16, 784, 9408, 39200, 62720, 37632, 7168, 256, 0, 18, 1152, 18816, 112896, 282240, 301056, 129024, 18432, 512
OFFSET
0,3
EXAMPLE
[0] 1;
[1] 0, 2;
[2] 0, 4, 4;
[3] 0, 6, 24, 8;
[4] 0, 8, 72, 96, 16;
[5] 0, 10, 160, 480, 320, 32;
[6] 0, 12, 300, 1600, 2400, 960, 64;
[7] 0, 14, 504, 4200, 11200, 10080, 2688, 128;
[8] 0, 16, 784, 9408, 39200, 62720, 37632, 7168, 256;
[9] 0, 18, 1152, 18816, 112896, 282240, 301056, 129024, 18432, 512.
MAPLE
aRow := n -> seq(binomial(n-1, k-1)*binomial(n, k)*2^k, k=0..n):
seq(print(aRow(n)), n=0..9);
MATHEMATICA
T[n_, k_] := Binomial[n-1, k-1] * Binomial[n, k] * 2^k;
Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten
PROG
(Python)
from math import comb
def T(n, k):
return comb(n-1, k-1)*comb(n, k)*2**k if k > 0 else k**n
print([T(n, k) for n in range(10) for k in range(n+1)]) # Michael S. Branicky, May 30 2021
CROSSREFS
Row sums are A002003 with a(0) = 1, cf. also A047781.
The coefficients of the associated polynomials are in A103371.
Sequence in context: A338896 A182059 A103328 * A167312 A114122 A319934
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, May 30 2021
STATUS
approved