A075878 Sum of coefficients of (x1)^(2i(1))*(x2)^(2i(2))*(x3)^(2i(3))*(x4)^(2i(4)) for {(i1),(i2),(i3),(i4)}=0,1,2,... : sum(i)=2n in the expansion of (x1+x2+x3+x4)^(2n) where n >= 1.

4, 40, 544, 8320, 131584, 2099200, 33562624, 536903680, 8590065664, 137439477760, 2199025352704, 35184380477440, 562949986975744, 9007199388958720, 144115188612726784, 2305843011361177600, 36893488156009037824, 590295810393065390080, 9444732965876729380864, 151115727452378402652160, 2417851639231457372667904

Offset: 1

Author

Jan Hagberg (jan.hagberg(AT)stat.su.se), Oct 16 2002

Keywords

• easy
• nonn

Comments

For k=3, the sequence divided by 3 is equal to A066443.

Crossrefs

Cf. A066443.

Essentially the same as A092812. - Kang Seonghoon (lifthrasiir(AT)gmail.com), Oct 09 2008

Programs

PARI

a(n, k=4) = 2^(1-k)*sum(r=0,floor((k-1)/2), binomial(k, r)*(k-2*r)^(2*n));
vector(33,n,a(n)) \\ Joerg Arndt, Apr 21 2025

Formula

a(n, 4) = 2^(1-4)*Sum_{r=0..floor((4-1)/2)} binomial(4, r)*(4-2*r)^(2*n).

a(n, k) = 2^(1-k)*Sum_{r=0..floor((k-1)/2)} binomial(k, r)*(k-2*r)^(2*n) for k>=1.

Extensions

Corrected by T. D. Noe, Nov 07 2006