A365218 G.f. satisfies A(x) = 1 + x*A(x)^6 / (1 + x*A(x)^6).

1, 1, 5, 34, 265, 2232, 19766, 181300, 1706737, 16392049, 159959240, 1581278838, 15800619070, 159321921844, 1618981274136, 16562211506496, 170426473666497, 1762771226922775, 18316562635133813, 191104193378725552, 2001224271292820200

Offset

0,3

Comments

Conjecture: Is a(n)>0 correct? It is correct up to the first 10000 terms.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..956

Formula

a(n) = Sum_{k=0..n} (-1)^k * 2^(n-k) * binomial(n,k) * binomial(6*n+k+1,n)/(6*n+k+1).

a(n) = Sum_{k=0..n} (-2)^(n-k) * binomial(6*n+k+1,k) * binomial(n-1,n-k)/(6*n+k+1).

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

Prog

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

Crossrefs

Cf. A291534, A364864, A364865, A364866.

Cf. A002296.

Sequence in context: A333804 A081342 A248055 * A243659 A365183 A371391

Adjacent sequences: A365215 A365216 A365217 * A365219 A365220 A365221

Keyword

nonn

Author

Seiichi Manyama, Aug 26 2023

Status

approved