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.

A028339 Coefficient of x^2 in expansion of (x+1)*(x+3)*...*(x+2*n-1).

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%I A028339 #19 Oct 18 2017 05:00:50
%S A028339 1,9,86,950,12139,177331,2924172,53809164,1094071221,24372200061,
%T A028339 590546123298,15467069396610,435512515705695,13121113142970855,
%U A028339 421214220916438680,14354510691610713240,517596339235489288425,19688993487602867898225,787995759739909824183150
%N A028339 Coefficient of x^2 in expansion of (x+1)*(x+3)*...*(x+2*n-1).
%C A028339 Equals third left hand column of A161198 triangle divided by 4. - _Johannes W. Meijer_, Jun 08 2009
%H A028339 G. C. Greubel, <a href="/A028339/b028339.txt">Table of n, a(n) for n = 2..400</a>
%F A028339 a(n) = Sum_{i=k+1,..,n}[ (-1)^(k+1-i) 2^(n-1) binomial(i-1, k) s1(n, i) ] with k = 2, where s1(n, i) are unsigned Stirling numbers of the first kind. - Victor Adamchik (adamchik(AT)ux10.sp.cs.cmu.edu), Jan 23 2001
%F A028339 E.g.f.: (log(1-2*x))^2/(8*sqrt(1-2*x)). - _Vladeta Jovovic_, Feb 19 2003
%F A028339 a(n) ~ n! * log(n)^2 * 2^(n-3) / sqrt(Pi*n) * (1 + (2*gamma + 4*log(2))/log(n)), where gamma is the Euler-Mascheroni constant (A001620). - _Vaclav Kotesovec_, Oct 18 2017
%e A028339 G.f. = x^2 + 9*x^3 + 86*x^4 + 950*x^5 + 12139*x^6 + 177331*x^7 + ...
%t A028339 Table[Coefficient[Product[x + 2*k - 1, {k, 1, n}], x, 2], {n,2,50}] (* _G. C. Greubel_, Nov 24 2016 *)
%o A028339 (PARI) a(n) = polcoeff(prod(k=1, n, x+2*k-1), 2); \\ _Michel Marcus_, Nov 12 2014
%Y A028339 Cf. A028338, A161198.
%K A028339 nonn
%O A028339 2,2
%A A028339 _Bill Gosper_
%E A028339 More terms from _Michel Marcus_, Nov 12 2014