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A298511 Central Lehmer-Comtet numbers of the first kind: a(n) = A008296(2n,n).

%I A298511 #16 Dec 01 2023 05:24:54
%S A298511 1,1,-1,-15,49,1365,-7645,-311311,2475473,132652377,-1367593305,
%T A298511 -90881245455,1151541572401,91341008892445,-1373222414339685,
%U A298511 -126594821384553375,2202549127844351265,231390624855674406705,-4573116447815658471025,-539278542630309415030735
%N A298511 Central Lehmer-Comtet numbers of the first kind: a(n) = A008296(2n,n).
%H A298511 Alois P. Heinz, <a href="/A298511/b298511.txt">Table of n, a(n) for n = 0..386</a>
%F A298511 a(n) = (2*n)!/n! * [x^(2*n)] ((1+x)*log(1+x))^n.
%F A298511 a(n) = Sum_{j=0..n} binomial(n+j,n) * n^j * Stirling1(2*n,n+j).
%p A298511 b:= proc(n, k) option remember; `if`(n=k, 1, `if`(k=0, 0,
%p A298511       (n-1)*b(n-2, k-1)+b(n-1, k-1)+(k-n+1)*b(n-1, k)))
%p A298511     end:
%p A298511 a:= n-> b(2*n, n):
%p A298511 seq(a(n), n=0..25);
%t A298511 b[n_, k_] := b[n, k] = If[n == k, 1, If[k == 0, 0,
%t A298511    (n-1) b[n-2, k-1] + b[n-1, k-1] + (k-n+1) b[n-1, k]]];
%t A298511 a[n_] := b[2n, n];
%t A298511 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Dec 01 2023, from Maple code *)
%Y A298511 Cf. A008275, A008296, A048994.
%K A298511 sign
%O A298511 0,4
%A A298511 _Alois P. Heinz_, Jan 20 2018