login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A328750 Constant term in the expansion of (-1 + (1 + w) * (1 + x) * (1 + y) * (1 + z) + (1 + 1/w) * (1 + 1/x) * (1 + 1/y) * (1 + 1/z))^n. 4

%I #15 Oct 28 2019 08:02:16

%S 1,1,31,391,8071,161671,3634921,84109201,2032357111,50355327991,

%T 1277302604521,32983865502721,864982811998801,22976755021842961,

%U 617140285389771391,16735405610179740151,457647302453165769751,12607719926638032161431,349620344754345216824041

%N Constant term in the expansion of (-1 + (1 + w) * (1 + x) * (1 + y) * (1 + z) + (1 + 1/w) * (1 + 1/x) * (1 + 1/y) * (1 + 1/z))^n.

%F a(n) = Sum_{i=0..n} (-1)^(n-i)*binomial(n,i)*Sum_{j=0..i} binomial(i,j)^5.

%F From _Vaclav Kotesovec_, Oct 28 2019: (Start)

%F Recurrence: n^4*(440*n^2 - 2728*n + 3723)*a(n) = (6600*n^6 - 54120*n^5 + 147013*n^4 - 174348*n^3 + 102442*n^2 - 29260*n + 3108)*a(n-1) + (194920*n^6 - 1988184*n^5 + 7650713*n^4 - 14588908*n^3 + 14793198*n^2 - 7658420*n + 1601964)*a(n-2) + (n-2)*(690800*n^5 - 7046160*n^4 + 26712814*n^3 - 47822370*n^2 + 40779795*n - 13361628)*a(n-3) + (n-3)*(n-2)*(975480*n^4 - 8974416*n^3 + 28602923*n^2 - 37477643*n + 16905924)*a(n-4) + (n-4)*(n-3)*(n-2)*(622600*n^3 - 4482720*n^2 + 9455173*n - 5628497)*a(n-5) + 341*(n-5)*(n-4)*(n-3)*(n-2)*(440*n^2 - 1848*n + 1435)*a(n-6).

%F a(n) ~ 31^(n+2) / (256 * sqrt(5) * Pi^2 * n^2). (End)

%t Table[Sum[(-1)^(n - i)*Binomial[n, i]*Sum[Binomial[i, j]^5, {j, 0, i}], {i, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Oct 28 2019 *)

%o (PARI) {a(n) = sum(i=0, n, (-1)^(n-i)*binomial(n,i)*sum(j=0, i, binomial(i, j)^5))}

%Y Column k=5 of A328747.

%Y Cf. A005261, A328751.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 27 2019

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)