A371616 -id:A371616 - cp's OEIS frontend

A371617 G.f. satisfies A(x) = ( 1 + x / (1 - x*A(x)^3)^3 )^2.

1, 2, 7, 54, 419, 3644, 33366, 317672, 3113559, 31200060, 318219653, 3292546660, 34475311605, 364621943538, 3889561661610, 41799988930926, 452126713579192, 4918321519144206, 53773399008883695, 590578523863692086, 6512515698908748358

Offset: 0

Seiichi Manyama, Mar 29 2024

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..934

Cf. A371613, A371615.

Cf. A371616.

a(n, r=2, s=3, t=0, u=6) = 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));

a(n) = Sum_{k=0..n} binomial(6*(n-k)+2,k) * binomial(n+2*k-1,n-k)/(3*(n-k)+1).

A365122 G.f. A(x) satisfies A(x) = (1 + x / (1 - x*A(x))^3)^3.

Original entry on oeis.org

1, 3, 12, 64, 372, 2319, 15105, 101649, 701073, 4929657, 35207220, 254690517, 1862325262, 13742311074, 102204992352, 765328009950, 5765316776550, 43661497944861, 332217854059362, 2538540859615095, 19471592691620310, 149871698475060433, 1157188723053901449

Offset: 0

Seiichi Manyama, Aug 22 2023

nonn

Cf. A006013, A365113.
Cf. A365119, A365121.
Cf. A371616.

a(n, s=3, t=3) = sum(k=0, n, binomial(t*(n-k+1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));

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

G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A371616. - Seiichi Manyama, Dec 06 2024

cp's OEIS Frontend

A371617 G.f. satisfies A(x) = ( 1 + x / (1 - x*A(x)^3)^3 )^2.

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