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A143185
Triangle read by rows: T(n, k) = (1 + abs(n-2*k))*binomial(n,k), with T(n, 0) = T(n, n) = 1.
1
1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 12, 6, 12, 1, 1, 20, 20, 20, 20, 1, 1, 30, 45, 20, 45, 30, 1, 1, 42, 84, 70, 70, 84, 42, 1, 1, 56, 140, 168, 70, 168, 140, 56, 1, 1, 72, 216, 336, 252, 252, 336, 216, 72, 1, 1, 90, 315, 600, 630, 252, 630, 600, 315, 90, 1
OFFSET
0,5
FORMULA
T(n, k) = (1 + abs(n-2*k))*binomial(n,k) for 1 <= k <= n-1, with T(n, 0) = T(n, n) = 1.
T(n, n-k) = T(n, k).
EXAMPLE
Table begins as:
1;
1, 1;
1, 2, 1;
1, 6, 6, 1;
1, 12, 6, 12, 1;
1, 20, 20, 20, 20, 1;
1, 30, 45, 20, 45, 30, 1;
1, 42, 84, 70, 70, 84, 42, 1;
1, 56, 140, 168, 70, 168, 140, 56, 1;
1, 72, 216, 336, 252, 252, 336, 216, 72, 1;
1, 90, 315, 600, 630, 252, 630, 600, 315, 90, 1;
MATHEMATICA
T[n_, k_] = If[k*(n-k)==0, 1, (1 + Abs[n-2*k])*Binomial[n, k]];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
PROG
(Magma)
A143185:= func< n, k | k eq 0 or k eq n select 1 else (1+Abs(n-2*k))*Binomial(n, k) >;
[A143185(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Apr 23 2024
(SageMath)
def A143185(n, k): return 1 if (k==0 or k==n) else (1+abs(n-2*k))*binomial(n , k)
flatten([[A143185(n, k) for k in range(n+1)] for n in range(13)]) # G. C. Greubel, Apr 23 2024
CROSSREFS
Sequence in context: A283795 A168641 A255914 * A347675 A157635 A075798
KEYWORD
nonn,tabl
AUTHOR
EXTENSIONS
Edited by G. C. Greubel, Apr 23 2024
STATUS
approved