%I
%S 1,1,2,19,74,68,1856,22717,182806,1095506,2706452,62235754,
%T 1630900556,28213310474,422792067164,5747245586467,
%U 68720160772442,602550199498622,1056275553274100,251539588303778798,9237652624016037908,263685036472764512992
%N Central terms in rows of triangle A219120.
%C The number of contiguous signs of the terms seems to grow roughly in proportion to the squareroot of the number of terms.
%H Paul D. Hanna, <a href="/A219121/b219121.txt">Table of n, a(n) for n = 1..200</a>
%F a(n) = [x^n] (1x)^(2*n1) * Sum_{k>=0} k^n *(k+1)^(k1) * exp((k+1)*x) * x^k/k!.
%e Triangle A219120 begins:
%e 1;
%e 1, 1, 1;
%e 1, 5, 2, 2, 1;
%e 1, 15, 13, 19, 3, 3, 1;
%e 1, 37, 128, 26, 74, 46, 4, 4, 1;
%e 1, 83, 679, 755, 654, 68, 230, 90, 5, 5, 1;
%e 1, 177, 2866, 9048, 2091, 5741, 1856, 498, 545, 155, 6, 6, 1; ...
%e in which the o.g.f. of row n, R(x,n), is given by:
%e R(x,n) = (1x)^(2*n1) * Sum_{k>=0} k^n *(k+1)^(k1) * exp((k+1)*x) * x^k/k!;
%e note that the coefficient of x^n in R(x,n), for n>=1, forms this sequence.
%e The signs of the terms of this sequence begin:
%e +,+,
%e ,,,,
%e +,+,+,+,+,
%e ,,,,,,,
%e +,+,+,+,+,+,+,+,+,+,
%e ,,,,,,,,,,,
%e +,+,+,+,+,+,+,+,+,+,+,+,+,
%e ,,,,,,,,,,,,,,
%e +,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,
%e ,,,,,,,,,,,,,,,,,
%e +,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,
%e ,,,,,,,,,,,,,,,,,,,
%e +,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+, ...
%o (PARI) {a(n)=polcoeff((1x)^(2*n1)*sum(k=0,2*n,(k^n)*(k+1)^(k1)*x^k/k!*exp((k+1)*x +x*O(x^n))),n)}
%o for(n=1,30,print1(a(n),", "))
%Y Cf. A219120.
%K sign
%O 1,3
%A _Paul D. Hanna_, Nov 13 2012
