This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A060190 #27 Aug 01 2024 01:53:17
%S A060190 1,76,1682,23548,259723,2485288,21707972,178300904,1403080725,
%T A060190 10708911188,79944249686,587172549764,4261002128223,30644790782352,
%U A060190 218917362275080,1556000598766224,11017646288488233,77790282457881756
%N A060190 A column and diagonal of A060187 (k=4).
%H A060190 G. C. Greubel, <a href="/A060190/b060190.txt">Table of n, a(n) for n = 4..1000</a>
%H A060190 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.
%H A060190 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (30,-385,2776,-12418,35908,-67818,82552,-62109,26190,-4725).
%F A060190 From _Wolfdieter Lang_, Apr 17 2017: (Start)
%F A060190 a(n) = A060187(n, 4), n >= 4, and 0 for n < 4,
%F A060190 a(n) = A060187(n, n-3), n >= 4, and 0 for n < 4.
%F A060190 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 A060190 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)
%F A060190 a(n) = Sum_{k=0..3} (-1)^k*binomial(n,k)*(7-2*k)^(n-1). - _G. C. Greubel_, Aug 01 2024
%p A060190 r := proc(n, k) option remember;
%p A060190 if n = 0 then if k = 0 then 1 else 0 fi else
%p A060190 (2*(n-k)+1)*r(n-1, k-1) + (2*k+1)*r(n-1, k) fi end:
%p A060190 A060189 := n -> r(n-1, 3): seq(A060189(n), n = 4..21); # _Peter Luschny_, May 06 2013
%t A060190 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 *)
%t A060190 A060190[n_]:= Sum[(-1)^k*Binomial[n,k]*(7-2*k)^(n-1), {k,0,3}];
%t A060190 Table[A060190[n], {n,4,40}] (* _G. C. Greubel_, Aug 01 2024 *)
%o A060190 (Magma)
%o A060190 [(&+[(-1)^k*Binomial(n,k)*(7-2*k)^(n-1): k in [0..3]]): n in [4..40]]; // _G. C. Greubel_, Aug 01 2024
%o A060190 (SageMath)
%o A060190 [sum((-1)^k*binomial(n,k)*(7-2*k)^(n-1) for k in range(4)) for n in range(4,40)] # _G. C. Greubel_, Aug 01 2024
%Y A060190 Cf. A060187.
%K A060190 nonn,easy
%O A060190 4,2
%A A060190 _N. J. A. Sloane_, Mar 20 2001
%E A060190 More terms from _Vladeta Jovovic_, Mar 20 2001