A378156 G.f. A(x) satisfies A(x) = ( 1 + x * A(x)^(1/2) * (1 + A(x)^(1/2)) )^4.

1, 8, 72, 720, 7728, 87104, 1017184, 12200640, 149429504, 1861059328, 23498407680, 300110580224, 3870135336192, 50323754919936, 659085377250816, 8686436702866432, 115120162870534144, 1533214282017157120, 20510220228874399744, 275462154992599851008, 3712900128220039372800

Offset

0,2

Links

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

Formula

G.f.: B(x)^4 where B(x) is the g.f. of A219534.

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

Prog

(PARI) a(n, r=4, t=2, u=2) = r*sum(k=0, n, binomial(n, k)*binomial(t*n+u*k+r, n)/(t*n+u*k+r));

Crossrefs

Cf. A219534, A371693, A378155.

Sequence in context: A165323 A082366 A221159 * A049388 A014479 A377678

Adjacent sequences: A378153 A378154 A378155 * A378157 A378158 A378159

Keyword

nonn

Author

Seiichi Manyama, Nov 18 2024

Status

approved