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%I #22 Nov 22 2021 12:26:39
%S 1,76,1682,23548,259723,2485288,21707972,178300904,1403080725,
%T 10708911188,79944249686,587172549764,4261002128223,30644790782352,
%U 218917362275080,1556000598766224,11017646288488233,77790282457881756
%N A column and diagonal of A060187 (k=4).
%H P. A. MacMahon, <a href="http://dx.doi.org/10.1112/plms/s2-19.1.305">The divisors of numbers</a>, Proc. London Math. Soc., (2) 19 (1921), 305-340; Coll. Papers II, pp. 267-302.
%F From _Wolfdieter Lang_, Apr 17 2017: (Start)
%F a(n) = A060187(n, 4), n >= 4, and 0 for n < 4,
%F a(n) = A060187(n, n-3), n >= 4, and 0 for n < 4.
%F O.g.f.: x^4*(1 + 46*x - 213*x^2 - 428*x^3 + 2295*x^4 - 1794*x^5 - 675*x^6) / Product_{j=0..3} (1 - (1+2*j)*x)^(4-j).
%F E.g.f.: (exp(7*x) - 7*x*exp(5*x) + (21*x^2/2)*exp(3*x) - (7*x^3/3!)*exp(x) - 1)/7. (End)
%p r := proc(n, k) option remember;
%p if n = 0 then if k = 0 then 1 else 0 fi else
%p (2*(n-k)+1)*r(n-1, k-1) + (2*k+1)*r(n-1, k) fi end:
%p A060189 := n -> r(n-1, 3): seq(A060189(n), n = 4..21); # _Peter Luschny_, May 06 2013
%t r[n_, k_] := r[n, k] = If[n == 0, If[k == 0, 1, 0], (2*(n-k)+1)*r[n-1, k-1] + (2*k+1)*r[n-1, k]]; A060189[n_] := r[n-1, 3]; Table[A060189[n], {n, 4, 21}] (* _Jean-François Alcover_, Dec 03 2013, translated from _Peter Luschny_'s program *)
%K nonn,easy
%O 4,2
%A _N. J. A. Sloane_, Mar 20 2001
%E More terms from _Vladeta Jovovic_, Mar 20 2001
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