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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 Table of n, a(n) for n=0..18. 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 Cf. A358108, A143583. Sequence in context: A170701 A170739 A218722 * A358853 A158534 A171325 Adjacent sequences: A358106 A358107 A358108 * A358110 A358111 A358112 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.)