A371675 G.f. satisfies A(x) = 1 + x * A(x)^(3/2) * (1 + A(x)^(1/2))^2.

1, 4, 32, 324, 3696, 45316, 583152, 7769348, 106250144, 1482925956, 21037812352, 302478044996, 4397824031376, 64549296707460, 955150116019920, 14233474784850948, 213417133281087040, 3217460713030341892, 48741781832765496288, 741606216370357708612

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

G.f. satisfies A(x) = ( 1 + x * A(x)^(3/2) * (1 + A(x)^(1/2)) )^2.

G.f.: B(x)^2 where B(x) is the g.f. of A144097.

a(n) = 2 * Sum_{k=0..n} binomial(n,k) * binomial(3*n+k+2,n)/(3*n+k+2).

a(n) ~ sqrt((88 + 161*sqrt(2/5))/Pi) * (223 + 70*sqrt(10))^n / (n^(3/2) * 3^(3*n + 5/2)). - Vaclav Kotesovec, Nov 28 2024

Prog

(PARI) a(n, r=2, t=3, u=1) = r*sum(k=0, n, binomial(n, k)*binomial(t*n+u*k+r, n)/(t*n+u*k+r));

Crossrefs

Column k=2 of A378238.

Cf. A006319, A032349, A371676. A371677, A371678.

Cf. A144097, A371679.

Sequence in context: A289427 A090004 A357404 * A061631 A291342 A099912

Adjacent sequences: A371672 A371673 A371674 * A371676 A371677 A371678

Keyword

nonn

Author

Seiichi Manyama, Apr 02 2024

Status

approved