A381913 Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / B(x) ), where B(x) is the g.f. of A001764.

1, 4, 28, 245, 2422, 25860, 291106, 3405405, 41014131, 505344113, 6341182427, 80768735045, 1041645452650, 13575670575944, 178528253213469, 2366073408348545, 31571528771106126, 423794981085407622, 5718929869862880055, 77539914280883389432, 1055790501909183080512

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))^3.

a(n) = Sum_{k=0..n} binomial(n+3*k+1,k) * binomial(4*n-k+2,n-k)/(n+3*k+1).

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(4*n-k+2, n-k)/(n+3*k+1));

Crossrefs

Cf. A381911, A381912.

Cf. A381880, A381916.

Cf. A001764.

Sequence in context: A229644 A354602 A228714 * A371693 A230640 A300050

Adjacent sequences: A381910 A381911 A381912 * A381914 A381915 A381916

Keyword

nonn,new

Author

Seiichi Manyama, Mar 10 2025

Status

approved