A381915 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / B(x) ), where B(x) is the g.f. of A002293.

1, 3, 18, 145, 1378, 14515, 163700, 1936414, 23716654, 298216851, 3827542585, 49938733635, 660366743580, 8830549084588, 119205253249287, 1622258295003714, 22232669093660250, 306569446979862205, 4250285556933578693, 59210418891925845529, 828417259759216617257

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

G.f. A(x) satisfies A(x) = B(x*A(x)) / (1 - x*A(x))^2.

a(n) = Sum_{k=0..n} binomial(n+4*k+1,k) * binomial(3*n-k+1,n-k)/(n+4*k+1).

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+4*k+1, k)*binomial(3*n-k+1, n-k)/(n+4*k+1));

Crossrefs

Cf. A381914, A381916.

Cf. A381879, A381912.

Cf. A002293.

Sequence in context: A289428 A123308 A374864 * A379099 A177383 A074525

Adjacent sequences: A381912 A381913 A381914 * A381916 A381921 A381922

Keyword

nonn,new

Author

Seiichi Manyama, Mar 10 2025

Status

approved