OFFSET
0,2
FORMULA
a(n) = (2*n)! [x^n] BesselI(0, 2*sqrt(x))^5.
a(n) = binomial(2*n,n)*A169714(n).
a(n) ~ 2^(2*n) * 5^(2*n + 5/2) / (16 * Pi^(5/2) * n^(5/2)). - Vaclav Kotesovec, Nov 13 2017
a(n) = Sum_{i+j+k+l+m=n, 0<=i,j,k,l,m<=n} multinomial(2n, [i,i,j,j,k,k,l,l,m,m]). - Shel Kaphan, Jan 24 2023
MAPLE
MATHEMATICA
Table[SeriesCoefficient[BesselI[0, 2 Sqrt[x]]^5, {x, 0, n}] (2 n) !, {n, 0, 15}]
Table[Binomial[2n, n]^2 Sum[(Binomial[n, j]^4/Binomial[2n, 2j]) HypergeometricPFQ[{-j, -j, -j}, {1, 1/2-j}, 1/4], {j, 0, n}], {n, 0, 15}]
Table[Sum[(2 n)!/(i! j! k! l! (n-i-j-k-l)!)^2, {i, 0, n}, {j, 0, n-i}, {k, 0, n-i-j}, {l, 0, n-i-j-k}], {n, 0, 30}] (* Shel Kaphan, Jan 24 2023 *)
CROSSREFS
KEYWORD
nonn,easy,walk
AUTHOR
Peter Luschny, May 23 2017
EXTENSIONS
Moved original definition to formula section and reworded definition descriptively similar to sequence A039699, by Dave R.M. Langers, Oct 12 2022
STATUS
approved