[go: up one dir, main page]

login
A365341
a(n) = (5*n)!/(4*n+1)!.
7
1, 1, 10, 210, 6840, 303600, 17100720, 1168675200, 93963542400, 8691104822400, 909171781056000, 106137499051584000, 13679492361575040000, 1929327666754295808000, 295570742023171270656000, 48877281133334949335040000, 8677556868736487617966080000
OFFSET
0,3
FORMULA
E.g.f.: exp( 1/5 * Sum_{k>=1} binomial(5*k,k) * x^k/k ). - Seiichi Manyama, Feb 08 2024
a(n) = A000142(n)*A002294(n). - Alois P. Heinz, Feb 08 2024
From Seiichi Manyama, Aug 31 2024: (Start)
E.g.f. satisfies A(x) = 1/(1 - x*A(x)^4).
a(n) = Sum_{k=0..n} (4*n+1)^(k-1) * |Stirling1(n,k)|. (End)
PROG
(PARI) a(n) = (5*n)!/(4*n+1)!;
(Python)
from sympy import ff
def A365341(n): return ff(5*n, n-1) # Chai Wah Wu, Sep 01 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Sep 01 2023
STATUS
approved