A028340 Coefficient of x^3 in expansion of (x+1)*(x+3)*...*(x+2*n-1).

1, 16, 230, 3480, 57379, 1038016, 20570444, 444647600, 10431670821, 264300628944, 7198061846898, 209814739262856, 6520139954328519, 215245451727154944, 7524314127912551832, 277705505168550027360, 10792700030471840300745, 440604294676004639627280

Offset: 3

Author

Bill Gosper

Keywords

• nonn

Comments

Equals fourth left hand column of A161198 triangle divided by 8. - Johannes W. Meijer, Jun 08 2009

Links

• G. C. Greubel, Table of n, a(n) for n = 3..400

Crossrefs

Cf. A028338, A161198.

Programs

Mathematica

Table[Coefficient[Product[x + 2*k - 1, {k, 1, n}], x, 3], {n,3,50}] (* G. C. Greubel, Nov 24 2016 *)

PARI

a(n) = polcoeff(prod(k=1, n, x+2*k-1), 3); \\ 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 = 3, 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))^3/( 48*sqrt(1-2*x) ). - Vladeta Jovovic, Feb 19 2003

Extensions

More terms from Michel Marcus, Nov 12 2014