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A375292
Expansion of 1/sqrt((1 - x + x^3)^2 + 4*x^4).
3
1, 1, 1, 0, -3, -8, -14, -15, 1, 51, 146, 261, 286, -24, -1029, -2975, -5375, -5930, 591, 22014, 63886, 115947, 128183, -14595, -486466, -1413161, -2569868, -2840890, 361667, 10972167, 31861581, 57980426, 64018181, -8985428, -250991300, -727998021, -1324662165
OFFSET
0,5
FORMULA
n*a(n) = (2*n-1)*a(n-1) - (n-1)*a(n-2) - (2*n-3)*a(n-3) - 2*(n-2)*a(n-4) - (n-3)*a(n-6).
a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(n-2*k,k)^2.
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(1/sqrt((1-x+x^3)^2+4*x^4))
(PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(n-2*k, k)^2);
CROSSREFS
Cf. A246840.
Sequence in context: A305179 A106386 A000232 * A361363 A067789 A225400
KEYWORD
sign
AUTHOR
Seiichi Manyama, Aug 10 2024
STATUS
approved