A389273 Expansion of (1/x) * Series_Reversion( x / ((1+x)^4 * (x+(1+x)^3)) ).

1, 8, 89, 1153, 16297, 243715, 3791505, 60733129, 994948474, 16592789186, 280757823701, 4807954970431, 83172997476850, 1451294503661088, 25513440249869331, 451449906880609004, 8034119597807304134, 143705636693844433196, 2582140632208806025722

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+1,k) * binomial(7*n-3*k+7,n-k).

a(n) = (1/(n+1)) * [x^n] ((1+x)^4 * (x+(1+x)^3))^(n+1).

a(n) = binomial(7*(1+n), n)*hypergeom([-(7+6*n)/2, -3*(1+n), -(1+n), -n], [-7*(1+n)/3, -(6+7*n)/3, -(5+7*n)/3], -2^2/3^3)/(1 + n). - Stefano Spezia, Sep 28 2025

Mathematica

Table[(1/(n+1)) Coefficient[((1+ x)^4* (x+(1+x)^3))^(n+1), x, n], {n, 0, 35}] (* Vincenzo Librandi, Sep 29 2025 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x/((1+x)^4*(x+(1+x)^3)))/x)
(Magma) R<x> := PolynomialRing(Rationals()); [ (1/(n+1))*Coefficient((((1+ x)^4* (x+(1+x)^3))^(n+1)), n) : n in [0..30] ]; // Vincenzo Librandi, Sep 29 2025

Crossrefs

Cf. A364747, A365192, A388730.

Cf. A387432.

Sequence in context: A184756 A295244 A379546 * A386769 A264072 A303056

Adjacent sequences: A389270 A389271 A389272 * A389274 A389275 A389276

Keyword

nonn

Author

Seiichi Manyama, Sep 28 2025

Status

approved