OFFSET
1,2
COMMENTS
This sequence is of the form (k^n - 1)/(k - 1) with k = 2*n + 1. See crossrefs in A218722 for other sequences of the same form.
FORMULA
a(n) = Sum_{i=0..n-1} A005408(n)^i.
a(n) = n! * [x^n] exp(x)*(exp(2*n*x) - 1)/(2*n).
a(n) = n! * [x^n] exp((n+1)*x)*sinh(n*x)/n.
Limit_{n->oo} a(n+1)/(n*a(n)) = 2*e.
Limit_{n->oo} (a(n+1)/a(n) - a(n)/a(n-1)) = 2*e.
MATHEMATICA
Table[((2n+1)^n-1)/(2n), {n, 20}]
PROG
(Python)
def A361291(n): return (((n<<1)+1)**n-1)//(n<<1) # Chai Wah Wu, Mar 14 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Stefano Spezia, Mar 12 2023
STATUS
approved