A382516 Expansion of 1/(1 - x/(1 - 9*x)^(4/3)).
1, 1, 13, 151, 1693, 18688, 204631, 2230498, 24246229, 263112874, 2852058448, 30892668295, 334454025715, 3619669508056, 39164977065622, 423695451762664, 4583082589819489, 49570596449054509, 536121822834121354, 5798064369702626227, 62702959640721355228
Offset: 0
Programs
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PARI
a(n) = sum(k=0, n, 9^(n-k)*binomial(n+k/3-1, n-k));
Formula
a(n) = Sum_{k=0..n} 9^(n-k) * binomial(n+k/3-1,n-k).
D-finite with recurrence (n-1)*(n-2)*a(n) -3*(n-2)*(17*n-35)*a(n-1) +27*(39*n^2-197*n+252)*a(n-2) +2*(-5468*n^2+32199*n-46873)*a(n-3) +6*(9115*n^2-56514*n+77702)*a(n-4) +54*(-1094*n^2-359*n+28901)*a(n-5) +54*(-9846*n^2+134559*n-449254)*a(n-6) +177147*(3*n-19)*(3*n-20)*a(n-7)=0. - R. J. Mathar, Mar 31 2025