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A376072 a(n) are half the sums of the gamma coefficients of the n-th row-generating function of triangle A375853.

%I A376072 #40 Sep 27 2024 10:15:39
%S A376072 1,4,18,68,251,888,3076,10456,35061,116252,381974,1245564,4035631,
%T A376072 13003696,41701512,133175792,423741161,1343864820,4249518490,
%U A376072 13402327540,42168298851,132388845224,414818381708,1297410683208,4051098663901,12629895834508,39319487031966,122247859681196
%N A376072 a(n) are half the sums of the gamma coefficients of the n-th row-generating function of triangle A375853.
%H A376072 Ming-Jian Ding and Jiang Zeng, <a href="https://arxiv.org/abs/2308.16782">Some new results on minuscule polynomial of type A</a>, arXiv:2308.16782, [math.CO], 2023.
%H A376072 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,2,-12,-9).
%F A376072 a(n) = 2^(n-1)*T_n((-1 + sqrt(3)*i)/2)/(1 + sqrt(3)*i)^n, where T_n(x) is the generating function of the n-th row of A375853.
%F A376072 a(n) = a(n - 1) + n*(3^(n-1) + (-1)^n)/8, a(2) = 1.
%F A376072 a(n) = ((2*n - 2)*a(n - 1) + 3*n*a(n - 2))/(n - 2), a(2) = 1, a(3) = 4.
%F A376072 a(n) = ((2*n - 1)*3^n + (2*n + 1)*(-1)^n)/32.
%F A376072 G.f.: x^2/(1 - 2*x - 3*x^2)^2.
%F A376072 E.g.f.: exp(x)*(2*x*cosh(2*x) - (1 - 4*x)*sinh(2*x))/16. - _Stefano Spezia_, Sep 23 2024
%e A376072 For n = 4, the row-generating function of triangle A375853(n, k) is 20*x + 56*x^2 + 20*x^3. Thus the corresponding gamma polynomial is 20*x + 16*x^2, and so a(4) = 18.
%p A376072 a := n -> (3^n*(2*n - 1) + (-1)^n*(2*n + 1))/32:
%p A376072 seq(a(n), n = 2..19);  # _Peter Luschny_, Sep 23 2024
%t A376072 LinearRecurrence[{4,2,-12,-9},{1,4,18,68},30]
%Y A376072 Cf. A375853.
%K A376072 nonn,easy
%O A376072 2,2
%A A376072 _Mingjian Ding_, Sep 08 2024