A378732 G.f. A(x) satisfies A(x) = ( 1 + x / (1 - x*A(x)) )^4.

1, 4, 10, 36, 155, 704, 3384, 16844, 86097, 449344, 2384170, 12822556, 69743953, 382982940, 2120323014, 11822279232, 66327376437, 374162700460, 2120999728610, 12075668658000, 69021358842795, 395909382981572, 2278286453089574, 13149207655326372, 76096242994616990

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

G.f.: A(x) = (1 + x*B(x))^4 where B(x) is the g.f. of A364743.

If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s )^r, then a(n) = r * Sum_{k=0..n} binomial(t*k+u*(n-k)+r,k) * binomial(n+(s-1)*k-1,n-k)/(t*k+u*(n-k)+r).

Prog

(PARI) a(n, r=4, s=1, t=0, u=4) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));

Crossrefs

Cf. A364743, A371612, A378731.

cf. A365118, A365119.

Sequence in context: A149186 A345245 A197552 * A052572 A079725 A154152

Adjacent sequences: A378729 A378730 A378731 * A378733 A378734 A378735

Keyword

nonn

Author

Seiichi Manyama, Dec 05 2024

Status

approved