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A155494 Triangle T(n, k) = (k+1)*(n-k+1)*binomial(n,k) with T(n, 0) = T(n, n) = 1, read by rows. 1
1, 1, 1, 1, 8, 1, 1, 18, 18, 1, 1, 32, 54, 32, 1, 1, 50, 120, 120, 50, 1, 1, 72, 225, 320, 225, 72, 1, 1, 98, 378, 700, 700, 378, 98, 1, 1, 128, 588, 1344, 1750, 1344, 588, 128, 1, 1, 162, 864, 2352, 3780, 3780, 2352, 864, 162, 1, 1, 200, 1215, 3840, 7350, 9072, 7350, 3840, 1215, 200, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
FORMULA
T(n, k) = (k+1)*(n-k+1)*binomial(n,k) with T(n, 0) = T(n, n) = 1.
Sum_{k=0..n} T(n, k) = 2^(n-2)*(n^2 +3*n +4) -2*n. - G. C. Greubel, May 27 2021
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 8, 1;
1, 18, 18, 1;
1, 32, 54, 32, 1;
1, 50, 120, 120, 50, 1;
1, 72, 225, 320, 225, 72, 1;
1, 98, 378, 700, 700, 378, 98, 1;
1, 128, 588, 1344, 1750, 1344, 588, 128, 1;
1, 162, 864, 2352, 3780, 3780, 2352, 864, 162, 1;
1, 200, 1215, 3840, 7350, 9072, 7350, 3840, 1215, 200, 1;
MATHEMATICA
T[n_, k_]:= If[k*(n-k)==0, 1, (k+1)*(n-k+1)*Binomial[n, k]];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, May 27 2021 *)
PROG
(Magma)
A155494:= func< n, k | k eq 0 or k eq n select 1 else (k+1)*(n-k+1)*Binomial(n, k) >;
[A155494(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, May 27 2021
(Sage)
def A155494(n, k): return 1 if (k==0 or k==n) else (k+1)*(n-k+1)*binomial(n, k)
flatten([[A155494(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, May 27 2021
CROSSREFS
Sequence in context: A174125 A051425 A051469 * A154227 A166340 A157178
KEYWORD
nonn,tabl,easy
AUTHOR
Roger L. Bagula, Jan 23 2009
EXTENSIONS
Edited by G. C. Greubel, May 27 2021
STATUS
approved

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Last modified June 13 22:21 EDT 2024. Contains 373391 sequences. (Running on oeis4.)