cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A358695 a(n) = numerator( Sum_{k=0..n} (-1)^k * binomial(1/2, k)^2 * binomial(n, k) ).

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%I A358695 #12 Dec 09 2022 03:54:44
%S A358695 1,3,33,75,1305,-8253,-340711,-2173509,-758532375,-3823240245,
%T A358695 -73518428511,-342444310533,-24952606638687,-111735599023125,
%U A358695 -1975318542049815,-8639356601706213,-9590905885722547959,-41296955508208952901,-707029904720030040775,-3010762771187568788685
%N A358695 a(n) = numerator( Sum_{k=0..n} (-1)^k * binomial(1/2, k)^2 * binomial(n, k) ).
%F A358695 a(n) = numerator(hypergeometric([-1/2, -1/2, -n], [1, 1], 1)).
%F A358695 a(n) = numerator(A358113(n) / 16^n). - _Andrey Zabolotskiy_, Dec 08 2022
%p A358695 a := n -> numer(simplify(hypergeom([-1/2, -1/2, -n], [1, 1], 1))):
%p A358695 seq(a(n), n = 0..19);
%t A358695 a[n_] := Numerator[HypergeometricPFQ[{-1/2, -1/2, -n}, {1, 1}, 1]]; Array[a, 20, 0] (* _Amiram Eldar_, Dec 08 2022 *)
%Y A358695 Cf. A056982 (denominators), A260832, A358113.
%K A358695 sign,frac
%O A358695 0,2
%A A358695 _Peter Luschny_, Dec 08 2022