A373278 Expansion of 1 / ( (1 - 9*x^3) * (1 - x/(1 - 9*x^3)^(1/3)) ).

1, 1, 1, 10, 13, 16, 100, 148, 205, 1000, 1606, 2410, 10000, 17005, 27070, 100000, 177421, 295648, 1000000, 1833178, 3168538, 10000000, 18811948, 33503020, 100000000, 192080866, 350707345, 1000000000, 1953820210, 3642942040, 10000000000, 19815499120, 37611477133

Offset

0,4

Links

Table of n, a(n) for n=0..32.

Formula

a(3*n) = 10^n for n >= 0.

a(n) = Sum_{k=0..floor(n/3)} 9^k * binomial(n/3,k).

a(n) == 1 (mod 3).

D-finite with recurrence (n-1)*(n-2)*a(n) +2*(-14*n^2+69*n-91)*a(n-3) +9*(n-3)*(29*n-114)*a(n-6) -810*(n-3)*(n-6)*a(n-9)=0. - R. J. Mathar, Jun 21 2024

Prog

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

Crossrefs

Cf. A000079, A100095, A373583, A373621.

Cf. A011557, A371458.

Sequence in context: A282108 A306035 A339077 * A335016 A240109 A163652

Adjacent sequences: A373275 A373276 A373277 * A373279 A373280 A373281

Keyword

nonn

Author

Seiichi Manyama, Jun 11 2024

Status

approved