A371490 Expansion of 1/(1 - x/(1 - 8*x)^(1/4)).

1, 1, 3, 15, 91, 601, 4155, 29553, 214303, 1575931, 11712599, 87776507, 662224819, 5023611579, 38284084575, 292892970967, 2248271735299, 17307950940833, 133580448494227, 1033263820897777, 8008342899292167, 62179343789159945, 483553052098053915

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..1104

Formula

a(n) = Sum_{k=0..n} 8^k * binomial((n+3*k)/4-1,k).

D-finite with recurrence (18432*n^3 + 82944*n^2 + 114048*n + 46656)*a(n) + (-13056*n^3 - 103680*n^2 - 261168*n - 209424)*a(n + 1) + (3680*n^3 + 41616*n^2 + 152368*n + 180672)*a(n + 2) + (146940*n^3 + 656016*n^2 + 876348*n + 316872)*a(n + 3) + (-122844*n^3 - 911742*n^2 - 2199618*n - 1714740)*a(n + 4) + (42495*n^3 + 436587*n^2 + 1479966*n + 1654464)*a(n + 5) + (-7808*n^3 - 101904*n^2 - 440656*n - 631680)*a(n + 6) + (804*n^3 + 12672*n^2 + 66228*n + 114840)*a(n + 7) + (-44*n^3 - 810*n^2 - 4942*n - 9996)*a(n + 8) + (n^3 + 21*n^2 + 146*n + 336)*a(n + 9). - Robert Israel, Jan 12 2026

Maple

h:= proc(n) local k;  add(8^k * binomial((n+3*k)/4-1, k), k=0..n) end proc:
map(h, [$0..30]); # Robert Israel, Jan 12 2026

Prog

(PARI) a(n) = sum(k=0, n, 8^k*binomial((n+3*k)/4-1, k));

Crossrefs

Cf. A373509.

Sequence in context: A077783 A347319 A047019 * A099251 A364740 A393601

Adjacent sequences: A371487 A371488 A371489 * A371491 A371492 A371493

Keyword

nonn

Author

Seiichi Manyama, Jun 07 2024

Status

approved