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Expansion of 1 / ( (1 - 16*x^4) * (1 - x/(1 - 16*x^4)^(1/4)) ).
3

%I #27 Jun 11 2024 15:49:30

%S 1,1,1,1,17,21,25,29,289,397,521,661,4913,7229,10137,13701,83521,

%T 129133,190249,269877,1419857,2280125,3492281,5149701,24137569,

%U 39950221,63153481,96159061,410338673,696126557,1129839065,1767607973,6975757441,12080257069

%N Expansion of 1 / ( (1 - 16*x^4) * (1 - x/(1 - 16*x^4)^(1/4)) ).

%F a(4*n) = 17^n for n >= 0.

%F a(n) = Sum_{k=0..floor(n/4)} 16^k * binomial(n/4,k).

%F a(n) == 1 (mod 4).

%o (PARI) a(n) = sum(k=0, n\4, 16^k*binomial(n/4, k));

%Y Cf. A000079, A100095, A373278, A373621.

%Y Cf. A373627.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Jun 11 2024