A028341 Coefficient of x^4 in expansion of (x+1)*(x+3)*...*(x+2*n-1).
1, 25, 505, 10045, 208054, 4574934, 107494190, 2702025590, 72578259391, 2078757113719, 63324503917311, 2046225352864875, 69953125893139644, 2523698606200763196, 95853765344939263692, 3824294822931302783964, 159940198124792648875341, 6998152417792503243516261
Offset: 4
Keywords
Examples
G.f. = x^4 + 25*x^5 + 505*x^6 + 10045*x^7 + 208054*x^8 + 4574934*x^9 + ...
Links
- Robert Israel, Table of n, a(n) for n = 4..369
Programs
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Maple
N:= 50: # to get a(4) to a(N) P[0]:= 1; for n from 1 to N do P[n]:= rem(P[n-1]*(x + 2*n-1), x^5,x) od: seq(coeff(P[n],x,4),n=4..N); # Robert Israel, Nov 13 2014
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Mathematica
Table[Coefficient[Product[x + 2*k - 1, {k, 1, n}], x, 4], {n,4,50}] (* G. C. Greubel, Nov 24 2016 *) -
PARI
a(n) = polcoeff(prod(k=1, n, x+2*k-1), 4); \\ Michel Marcus, Nov 12 2014
Formula
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
E.g.f.: (log(1-2*x))^4/( 384*sqrt(1-2*x) ). - Vladeta Jovovic, Feb 19 2003
Extensions
More terms from Michel Marcus, Nov 12 2014
Comments