A371723 -id:A371723 - cp's OEIS frontend

A370891 G.f. satisfies A(x) = ( 1 + x * A(x)^(1/4) * (1 + A(x)^(3/4)) )^2.

1, 4, 14, 52, 205, 844, 3588, 15632, 69434, 313264, 1431650, 6613732, 30834548, 144895284, 685566370, 3263309844, 15616322995, 75085908112, 362563417968, 1757412095456, 8548129677400, 41710100368160, 204110896990686, 1001480947876276, 4925833177966164

Offset: 0

Seiichi Manyama, Apr 04 2024

nonn

Cf. A000292, A371723.

Cf. A106228, A262441, A371724.

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

G.f.: B(x)^4 where B(x) is the g.f. of A106228.

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

A371725 G.f. satisfies A(x) = ( 1 + x * A(x)^(1/5) * (1 + A(x)) )^(5/2).

Original entry on oeis.org

1, 5, 25, 145, 925, 6266, 44245, 322075, 2399725, 18211775, 140285018, 1093997085, 8620125925, 68523526635, 548867710575, 4425604018075, 35892727867805, 292604563615625, 2396375011877275, 19707111724556025, 162671328783723678, 1347313142469049275

Offset: 0

Seiichi Manyama, Apr 04 2024

nonn

Cf. A370471, A370472, A371723.

Cf. A371724.

a(n) = sum(k=0, n, binomial(n, k)*binomial(n/2+5*k/2+5/2, n)/(n/5+k+1));

G.f.: B(x)^5 where B(x) is the g.f. of A370472.

a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n/2+5*k/2+5/2,n)/(n/5+k+1).

cp's OEIS Frontend

A370891 G.f. satisfies A(x) = ( 1 + x * A(x)^(1/4) * (1 + A(x)^(3/4)) )^2.

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