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A147716 Triangle of coefficients in expansion of (14 + x)^n.

%I A147716 #17 Sep 08 2022 08:45:38
%S A147716 1,14,1,196,28,1,2744,588,42,1,38416,10976,1176,56,1,537824,192080,
%T A147716 27440,1960,70,1,7529536,3226944,576240,54880,2940,84,1,105413504,
%U A147716 52706752,11294304,1344560,96040,4116,98,1,1475789056,843308032,210827008,30118144,2689120,153664,5488,112,1
%N A147716 Triangle of coefficients in expansion of (14 + x)^n.
%C A147716 Triangle T(n,k), read by rows, given by [14, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938.
%H A147716 G. C. Greubel, <a href="/A147716/b147716.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A147716 T(n,k) = binomial(n,k) * 14^(n-k).
%F A147716 G.f.: 1/(1 - 14*x - x*y). - _R. J. Mathar_, Aug 12 2015
%F A147716 Sum_{k=0..n} T(n, k) = 15^n = A001024(n). - _G. C. Greubel_, May 15 2021
%e A147716 Triangle begins :
%e A147716        1;
%e A147716       14,      1;
%e A147716      196,     28,     1;
%e A147716     2744,    588,    42,    1;
%e A147716    38416,  10976,  1176,   56,  1;
%e A147716   537824, 192080, 27440, 1960, 70, 1;
%t A147716 With[{m=8}, CoefficientList[CoefficientList[Series[1/(1-14*x-x*y), {x, 0, m}, {y, 0, m}], x], y]]//Flatten (* _Georg Fischer_, Feb 17 2020 *)
%o A147716 (Magma) [14^(n-k)*Binomial(n,k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, May 15 2021
%o A147716 (Sage) flatten([[14^(n-k)*binomial(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, May 15 2021
%Y A147716 Cf. A001024, A023531, A130595.
%Y A147716 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), this sequence (q=14), A027467 (q=15).
%K A147716 easy,nonn,tabl
%O A147716 0,2
%A A147716 _Philippe Deléham_, Nov 11 2008
%E A147716 a(36) corrected by _Georg Fischer_, Feb 17 2020