A393421 Expansion of (1/x) * Series_Reversion( x * (5 * (1 - x)^2 - 4) ).

1, 10, 195, 4750, 129575, 3787000, 115948500, 3671043750, 119208409375, 3948415006250, 132876931646875, 4530568869125000, 156171483961062500, 5433476411181250000, 190552224909681875000, 6729077034574033593750, 239073540989053618359375, 8539570155140047949218750, 306487923866488387353515625

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

G.f. A(x) satisfies A(x) = 1/(5 * (1 - x*A(x))^2 - 4).

a(n) = (1/(n+1)) * Sum_{k=0..n} 5^k * (-1)^(n-k) * (1/2)^(n-2*k) * binomial(n+k,k) * binomial(k,n-k).

D-finite with recurrence 16*n*(n+1)*a(n) -310*n*(2*n-1)*a(n-1) -15*(3*n-2)*(3*n-4)*a(n-2)=0. - R. J. Mathar, Feb 24 2026

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(5*(1-x)^2-4))/x)

Crossrefs

Cf. A006013, A393418, A393419, A393420.

Sequence in context: A252974 A341503 A187652 * A361311 A007816 A365176

Adjacent sequences: A393418 A393419 A393420 * A393422 A393423 A393424

Keyword

nonn

Author

Seiichi Manyama, Feb 14 2026

Status

approved