A390924 - OEIS

%I #15 Nov 24 2025 10:06:49

%S 1,8,70,680,7030,75296,824188,9154160,102748390,1162484240,

%T 13234625524,151434413552,1739968195900,20061852185600,

%U 232000158556600,2689767185663840,31254074218228870,363870436065071600,4243634227797304900,49567706611284604400,579776539644142145620

%N Expansion of 1/((1-2*x) * sqrt(1-12*x)).

%H Seiichi Manyama, <a href="/A390924/b390924.txt">Table of n, a(n) for n = 0..928</a>

%F a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(2*k,k).

%F n*a(n) = (14*n-6)*a(n-1) - 12*(2*n-1)*a(n-2).

%F a(n) = 2*a(n-1) + A098658(n).

%o (PARI) a(n) = sum(k=0, n, 3^k*2^(n-k)*binomial(2*k, k));

%Y Cf. A000984, A082590, A098658, A390921.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 24 2025