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

0,3

Links

Table of n, a(n) for n=0..20.

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

Prog

(PARI) a(n) = sum(k=0, n, 9^(n-k)*binomial(n+k/3-1, n-k));

Crossrefs

Cf. A362206, A362210, A382517.

Cf. A004991.

Sequence in context: A386359 A396245 A097168 * A305262 A296722 A252972

Adjacent sequences: A382513 A382514 A382515 * A382517 A382518 A382519

Keyword

nonn,easy

Author

Seiichi Manyama, Mar 30 2025

Status

approved