A379039 -id:A379039 - cp's OEIS frontend

A379037 G.f. A(x) satisfies A(x) = ( (1 + x) * (1 + x*A(x)^(3/2)) )^2.

1, 4, 18, 106, 689, 4782, 34707, 260190, 1999168, 15660176, 124596498, 1004110948, 8179379807, 67239070868, 557098881919, 4647368670950, 39001655222787, 329048378867468, 2789241880512898, 23743798316713368, 202894843070927859, 1739775692700850554

Offset: 0

Seiichi Manyama, Dec 14 2024

nonn

Cf. A004798, A073155, A379039.

Cf. A364336, A366200.

a(n) = 2*sum(k=0, n, binomial(3*k+2, k)*binomial(3*k+2, n-k)/(3*k+2));

G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A364336.

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

A379038 G.f. A(x) satisfies A(x) = ( (1 + x) * (1 + x*A(x)^(4/3)) )^3.

Original entry on oeis.org

1, 6, 39, 320, 2907, 28152, 284907, 2977116, 31875708, 347884085, 3855802689, 43283239650, 491083601338, 5622489637407, 64877058557079, 753705528179424, 8808460811302728, 103487549564845200, 1221565052783161763, 14480208437556590346, 172299129911222223324

Offset: 0

Seiichi Manyama, Dec 14 2024

nonn

Cf. A364337, A379039.

a(n) = 3*sum(k=0, n, binomial(4*k+3, k)*binomial(4*k+3, n-k)/(4*k+3));

G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A364337.

a(n) = 3 * Sum_{k=0..n} binomial(4*k+3,k) * binomial(4*k+3,n-k)/(4*k+3).

cp's OEIS Frontend

A379037 G.f. A(x) satisfies A(x) = ( (1 + x) * (1 + x*A(x)^(3/2)) )^2.

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