A370838 Expansion of (1/x) * Series_Reversion( x/(x+1/(1+x^4)) ).

1, 1, 1, 1, 0, -4, -14, -34, -64, -80, 16, 496, 1946, 5266, 10830, 14886, -884, -92564, -390404, -1113380, -2405649, -3529749, -360799, 20509101, 91770476, 271807476, 608858576, 941203576, 243522996, -4977842140, -23564569004, -72054072364, -166314098964

Offset: 0

Author

Seiichi Manyama, Mar 03 2024

Keywords

• sign

Links

• Index entries for reversions of series

Crossrefs

Cf. A370836, A370837.

Cf. A227035, A370801.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(serreverse(x/(x+1/(1+x^4)))/x)

PARI

a(n) = sum(k=0, n\4, (-1)^k*binomial(n, 4*k)*binomial(5*k, k)/(4*k+1));

Formula

a(n) = Sum_{k=0..floor(n/4)} (-1)^k * binomial(n,4*k) * binomial(5*k,k)/(4*k+1).