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A356651 Triangle read by rows. T(n, k) = [x^k](0^n + 4^n * ((1 - x)^(-1/2) - 1)).

%I A356651 #10 Sep 09 2022 04:06:21
%S A356651 1,0,2,0,8,6,0,32,24,20,0,128,96,80,70,0,512,384,320,280,252,0,2048,
%T A356651 1536,1280,1120,1008,924,0,8192,6144,5120,4480,4032,3696,3432,0,32768,
%U A356651 24576,20480,17920,16128,14784,13728,12870,0,131072,98304,81920,71680,64512,59136,54912,51480,48620
%N A356651 Triangle read by rows. T(n, k) = [x^k](0^n + 4^n * ((1 - x)^(-1/2) - 1)).
%F A356651 T(n, 0) = 0^n, T(n, n) = binomial(2*n, n), otherwise T(n, k) = 4^(n - k)*T(k, k).
%e A356651 [0] 1;
%e A356651 [1] 0,      2;
%e A356651 [2] 0,      8,     6;
%e A356651 [3] 0,     32,    24,    20;
%e A356651 [4] 0,    128,    96,    80,    70;
%e A356651 [5] 0,    512,   384,   320,   280,   252;
%e A356651 [6] 0,   2048,  1536,  1280,  1120,  1008,   924;
%e A356651 [7] 0,   8192,  6144,  5120,  4480,  4032,  3696,  3432;
%e A356651 [8] 0,  32768, 24576, 20480, 17920, 16128, 14784, 13728, 12870;
%e A356651 [9] 0, 131072, 98304, 81920, 71680, 64512, 59136, 54912, 51480, 48620;
%p A356651 ogf := n -> 0^n + 4^n * ((1 - x)^(-1/2) - 1):
%p A356651 ser := n -> series(ogf(n), x, 32):
%p A356651 seq(seq(coeff(ser(n), x, k), k = 0..n), n = 0..9);
%Y A356651 Cf. A000984, A004171, A172060 (row sums), A357012.
%K A356651 nonn,tabl
%O A356651 0,3
%A A356651 _Peter Luschny_, Sep 08 2022