A364339 G.f. satisfies A(x) = (1 + x) * (1 + x*A(x)^6).

1, 2, 13, 150, 1978, 28603, 438273, 6992052, 114915180, 1932233883, 33081722359, 574755965137, 10107627041697, 179576579730534, 3218352405778284, 58114340679967608, 1056284029850962674, 19310039426151335622, 354818596435147647654, 6549556302551204621664, 121394125733645986376838

Offset: 0

Author

Seiichi Manyama, Jul 19 2023

Keywords

• nonn

Crossrefs

Cf. A073157, A364336, A364337, A364338.

Cf. A239109, A364333, A364340.

Programs

Mathematica

terms = 21; A[] = 0; Do[A[x] = (1+x)(1+x*A[x]^6) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Mar 24 2025 *)

PARI

a(n) = sum(k=0, n, binomial(6*k+1, k)*binomial(6*k+1, n-k)/(6*k+1));

Formula

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