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%I #21 Sep 08 2022 08:44:49
%S 1,15,1,225,30,1,3375,675,45,1,50625,13500,1350,60,1,759375,253125,
%T 33750,2250,75,1,11390625,4556250,759375,67500,3375,90,1,170859375,
%U 79734375,15946875,1771875,118125,4725,105,1,2562890625,1366875000,318937500,42525000,3543750,189000,6300,120,1
%N Triangle whose (n,k)-th entry is 15^(n-k)*binomial(n,k).
%H G. C. Greubel, <a href="/A027467/b027467.txt">Rows n = 0..50 of the triangle, flattened</a>
%F Numerators of lower triangle of (a[i,j])^4 where a[i,j] = binomial(i-1, j-1)/2^(i-1) if j<=i, 0 if j>i.
%F Sum_{k=0..n} T(n,k)*x^k = (15 + x)^n.
%e Triangle begins:
%e 1;
%e 15, 1;
%e 225, 30, 1;
%e 3375, 675, 45, 1;
%e 50625, 13500, 1350, 60, 1;
%e 759375, 253125, 33750, 2250, 75, 1;
%e 11390625, 4556250, 759375, 67500, 3375, 90, 1;
%e 170859375, 79734375, 15946875, 1771875, 118125, 4725, 105, 1;
%e 2562890625, 1366875000, 318937500, 42525000, 3543750, 189000, 6300, 120, 1;
%t Table[Binomial[n,k]15^(n-k),{n,0,10},{k,0,n}]//Flatten (* _Harvey P. Dale_, Dec 31 2017 *)
%o (Magma) [(15)^(n-k)*Binomial(n,k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, May 12 2021
%o (Sage) flatten([[(15)^(n-k)*binomial(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, May 12 2021
%Y Sequences of the form q^(n-k)*binomial(n, k): A007318 (q=1), A038207 (q=2), A027465 (q=3), A038231 (q=4), A038243 (q=5), A038255 (q=6), A027466 (q=7), A038279 (q=8), A038291 (q=9), A038303 (q=10), A038315 (q=11), A038327 (q=12), A133371 (q=13), A147716 (q=14), this sequence (q=15).
%K nonn,tabl
%O 0,2
%A _Olivier Gérard_
%E Simpler definition from _Philippe Deléham_, Nov 10 2008
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