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A298511
Central Lehmer-Comtet numbers of the first kind: a(n) = A008296(2n,n).
3
1, 1, -1, -15, 49, 1365, -7645, -311311, 2475473, 132652377, -1367593305, -90881245455, 1151541572401, 91341008892445, -1373222414339685, -126594821384553375, 2202549127844351265, 231390624855674406705, -4573116447815658471025, -539278542630309415030735
OFFSET
0,4
LINKS
FORMULA
a(n) = (2*n)!/n! * [x^(2*n)] ((1+x)*log(1+x))^n.
a(n) = Sum_{j=0..n} binomial(n+j,n) * n^j * Stirling1(2*n,n+j).
MAPLE
b:= proc(n, k) option remember; `if`(n=k, 1, `if`(k=0, 0,
(n-1)*b(n-2, k-1)+b(n-1, k-1)+(k-n+1)*b(n-1, k)))
end:
a:= n-> b(2*n, n):
seq(a(n), n=0..25);
MATHEMATICA
b[n_, k_] := b[n, k] = If[n == k, 1, If[k == 0, 0,
(n-1) b[n-2, k-1] + b[n-1, k-1] + (k-n+1) b[n-1, k]]];
a[n_] := b[2n, n];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Dec 01 2023, from Maple code *)
CROSSREFS
KEYWORD
sign
AUTHOR
Alois P. Heinz, Jan 20 2018
STATUS
approved