A370891 -id:A370891 - cp's OEIS frontend

A371724 G.f. satisfies A(x) = ( 1 + x * A(x)^(1/3) * (1 + A(x)) )^(3/2).

1, 3, 9, 31, 117, 468, 1949, 8361, 36693, 163956, 743388, 3411576, 15816609, 73967637, 348517539, 1652896367, 7884305829, 37800279504, 182055056428, 880410972156, 4273376488956, 20811901707192, 101666716335912, 498035242836144, 2446003588237193, 12041562653655453

Offset: 0

Seiichi Manyama, Apr 04 2024

nonn

Cf. A106228, A262441, A370891.

Cf. A371725.

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

G.f.: B(x)^3 where B(x) is the g.f. of A106228.

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

A371723 G.f. satisfies A(x) = ( 1 + x * A(x)^(1/4) * (1 + A(x)^(5/4)) )^2.

Original entry on oeis.org

1, 4, 18, 100, 623, 4156, 29032, 209656, 1552535, 11724904, 89958000, 699213444, 5494103979, 43570067100, 348274269966, 2803139823512, 22698137859554, 184779492011244, 1511406790180350, 12415340284461312, 102377122022648745, 847144310799588732

Offset: 0

Seiichi Manyama, Apr 04 2024

nonn

Cf. A000292, A370891.

Cf. A370471, A370472, A371725.

a(n) = 2*sum(k=0, n, binomial(n, k)*binomial(n/2+5*k/2+2, n)/(n/2+5*k/2+2));

G.f.: B(x)^4 where B(x) is the g.f. of A370472.

a(n) = 2 * Sum_{k=0..n} binomial(n,k) * binomial(n/2+5*k/2+2,n)/(n/2+5*k/2+2).

cp's OEIS Frontend

A371724 G.f. satisfies A(x) = ( 1 + x * A(x)^(1/3) * (1 + A(x)) )^(3/2).

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