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A027467 Triangle whose (n,k)-th entry is 15^(n-k)*binomial(n,k).

%I A027467 #21 Sep 08 2022 08:44:49
%S A027467 1,15,1,225,30,1,3375,675,45,1,50625,13500,1350,60,1,759375,253125,
%T A027467 33750,2250,75,1,11390625,4556250,759375,67500,3375,90,1,170859375,
%U A027467 79734375,15946875,1771875,118125,4725,105,1,2562890625,1366875000,318937500,42525000,3543750,189000,6300,120,1
%N A027467 Triangle whose (n,k)-th entry is 15^(n-k)*binomial(n,k).
%H A027467 G. C. Greubel, <a href="/A027467/b027467.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A027467 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 A027467 Sum_{k=0..n} T(n,k)*x^k = (15 + x)^n.
%e A027467 Triangle begins:
%e A027467            1;
%e A027467           15,          1;
%e A027467          225,         30,         1;
%e A027467         3375,        675,        45,        1;
%e A027467        50625,      13500,      1350,       60,       1;
%e A027467       759375,     253125,     33750,     2250,      75,      1;
%e A027467     11390625,    4556250,    759375,    67500,    3375,     90,    1;
%e A027467    170859375,   79734375,  15946875,  1771875,  118125,   4725,  105,   1;
%e A027467   2562890625, 1366875000, 318937500, 42525000, 3543750, 189000, 6300, 120, 1;
%t A027467 Table[Binomial[n,k]15^(n-k),{n,0,10},{k,0,n}]//Flatten (* _Harvey P. Dale_, Dec 31 2017 *)
%o A027467 (Magma) [(15)^(n-k)*Binomial(n,k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, May 12 2021
%o A027467 (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 A027467 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 A027467 nonn,tabl
%O A027467 0,2
%A A027467 _Olivier Gérard_
%E A027467 Simpler definition from _Philippe Deléham_, Nov 10 2008