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.

A028341 Coefficient of x^4 in expansion of (x+1)*(x+3)*...*(x+2*n-1).

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%I A028341 #21 Nov 25 2016 13:33:14
%S A028341 1,25,505,10045,208054,4574934,107494190,2702025590,72578259391,
%T A028341 2078757113719,63324503917311,2046225352864875,69953125893139644,
%U A028341 2523698606200763196,95853765344939263692,3824294822931302783964,159940198124792648875341,6998152417792503243516261
%N A028341 Coefficient of x^4 in expansion of (x+1)*(x+3)*...*(x+2*n-1).
%C A028341 Equals fifth left hand column of A161198 triangle divided by 16. - _Johannes W. Meijer_, Jun 08 2009
%H A028341 Robert Israel, <a href="/A028341/b028341.txt">Table of n, a(n) for n = 4..369</a>
%F A028341 a(n) = Sum_{i=k+1,..,n} (-1)^(k+1-i)*2^(n-1)*binomial(i-1, k)*s1(n, i) with k = 4, 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 A028341 E.g.f.: (log(1-2*x))^4/( 384*sqrt(1-2*x) ). - _Vladeta Jovovic_, Feb 19 2003
%e A028341 G.f. = x^4 + 25*x^5 + 505*x^6 + 10045*x^7 + 208054*x^8 + 4574934*x^9 + ...
%p A028341 N:= 50: # to get a(4) to a(N)
%p A028341 P[0]:= 1;
%p A028341 for n from 1 to N do
%p A028341   P[n]:= rem(P[n-1]*(x + 2*n-1), x^5,x)
%p A028341 od:
%p A028341 seq(coeff(P[n],x,4),n=4..N); # _Robert Israel_, Nov 13 2014
%t A028341 Table[Coefficient[Product[x + 2*k - 1, {k, 1, n}], x, 4], {n,4,50}] (* _G. C. Greubel_, Nov 24 2016 *)
%o A028341 (PARI) a(n) = polcoeff(prod(k=1, n, x+2*k-1), 4); \\ _Michel Marcus_, Nov 12 2014
%Y A028341 Cf. A028338, A004041, A028339, A028340, A161198.
%K A028341 nonn
%O A028341 4,2
%A A028341 _Bill Gosper_
%E A028341 More terms from _Michel Marcus_, Nov 12 2014