OFFSET
0,3
COMMENTS
Main diagonal of A344567.
FORMULA
a(n) = Sum_{j=0..n} (n - 1)^j*binomial(n, j)*hypergeom([(j - n)/2, (j - n + 1)/2], [j + 2], 4).
a(n) ~ n^n * (1 + 1/n + 1/(2*n^2) - 4/(3*n^3) - 119/(24*n^4) - 1249/(120*n^5) - ...). - Vaclav Kotesovec, May 24 2021
MAPLE
aList := proc(len) 2 / (1 - (2*n - 1)*x + sqrt(1 - 2*x - 3*x^2));
seq(coeff(series(%, x, len+2), x, n), n = 0..len) end: aList(19);
MATHEMATICA
Unprotect[Power]; 0^0 := 1;
a[n_] := Sum[(n-1)^j Binomial[n, j] Hypergeometric2F1[(j - n)/2, (j - n + 1)/2, j + 2, 4], {j, 0, n}]; Table[a[n], {n, 0, 19}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, May 24 2021
STATUS
approved