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

4,2

Comments

Equals fifth left hand column of A161198 triangle divided by 16. - Johannes W. Meijer, Jun 08 2009

Links

Robert Israel, Table of n, a(n) for n = 4..369

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

Example

G.f. = x^4 + 25*x^5 + 505*x^6 + 10045*x^7 + 208054*x^8 + 4574934*x^9 + ...

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

Mathematica

Table[Coefficient[Product[x + 2*k - 1, {k, 1, n}], x, 4], {n, 4, 50}] (* G. C. Greubel, Nov 24 2016 *)

Prog

(PARI) a(n) = polcoeff(prod(k=1, n, x+2*k-1), 4); \\ Michel Marcus, Nov 12 2014

Crossrefs

Cf. A028338, A004041, A028339, A028340, A161198.

Sequence in context: A118445 A000497 A353116 * A282689 A282874 A144942

Adjacent sequences: A028338 A028339 A028340 * A028342 A028343 A028344

Keyword

nonn

Author

Bill Gosper

Extensions

More terms from Michel Marcus, Nov 12 2014

Status

approved