A364337 G.f. satisfies A(x) = (1 + x) * (1 + x*A(x)^4).

1, 2, 9, 68, 580, 5406, 53270, 545844, 5757332, 62094217, 681653493, 7591431752, 85558696024, 974024788280, 11184192097016, 129378232148016, 1506363564912368, 17639001584452320, 207593804132718948, 2454236122156830254, 29132714097692056954, 347086786035103983446

Offset: 0

Author

Seiichi Manyama, Jul 19 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..907

Crossrefs

Cf. A073157, A364336, A364338, A364339.

Cf. A215623, A215715, A234461, A239107.

Programs

Mathematica

terms = 22; A[] = 0; Do[A[x] = (1+x)(1+x*A[x]^4) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Mar 24 2025 *)

PARI

a(n) = sum(k=0, n, binomial(4*k+1, k)*binomial(4*k+1, n-k)/(4*k+1));

Formula

a(n) = Sum_{k=0..n} binomial(4*k+1,k) * binomial(4*k+1,n-k) / (4*k+1).