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A358109 a(n) = 16^n * Sum_{k=0..n} binomial(1/2, k)^2 * binomial(n, k). 2
1, 20, 388, 7376, 138340, 2572880, 47652240, 882388800, 16402291620, 307411770320, 5837516987920, 112918906836800, 2237687548230160, 45677390764531520, 964818477552462400, 21148251536958233856, 481370160754727691300, 11360399185583414128848, 277079154699775861823376 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Belongs to the family of Apéry-like sequences.
LINKS
FORMULA
a(n) = 16^n * hypergeom([-1/2, -1/2, -n], [1, 1], -1).
a(n) ~ 2^(5*n + 1) / (Pi * n^3). - Vaclav Kotesovec, Nov 12 2022
MAPLE
a := n -> 16^n*add(binomial(1/2, k)^2*binomial(n, k), k = 0..n):
seq(a(n), n = 0..18);
MATHEMATICA
a[n_] := 16^n * HypergeometricPFQ[{-1/2, -1/2, -n}, {1, 1}, -1]; Array[a, 19, 0] (* Amiram Eldar, Nov 12 2022 *)
PROG
(Python)
from sympy import binomial, S
def A358109(n): return (1<<(n<<2))*sum(binomial(S.Half, k)**2*binomial(n, k) for k in range(n+1)) # Chai Wah Wu, Nov 13 2022
CROSSREFS
Sequence in context: A170701 A170739 A218722 * A358853 A158534 A171325
KEYWORD
nonn
AUTHOR
Peter Luschny, Nov 12 2022
STATUS
approved

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Last modified May 21 08:47 EDT 2024. Contains 372732 sequences. (Running on oeis4.)