cp's OEIS Frontend

A377399 Expansion of e.g.f. (2 - exp(x))^4.

%I A377399 #19 Oct 27 2024 23:44:27
%S A377399 1,-4,8,8,-40,-184,-232,1928,19160,116936,600728,2826248,12623960,
%T A377399 54550856,230564888,959736968,3952166360,16149893576,65626404248,
%U A377399 265592398088,1071642518360,4314414017096,17341238230808,69615800073608,279215943071960,1119122403273416
%N A377399 Expansion of e.g.f. (2 - exp(x))^4.
%H A377399 Seiichi Manyama, <a href="/A377399/b377399.txt">Table of n, a(n) for n = 0..1000</a>
%H A377399 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-35,50,-24).
%F A377399 a(n) = 9*a(n-1) - 26*a(n-2) + 24*a(n-3) + 192 for n > 3.
%F A377399 a(n) = Sum_{k=0..4} (-1)^k * k! * binomial(4,k) * Stirling2(n,k).
%F A377399 a(n) = Sum_{k=0..4} (-1)^k * 2^(4-k) * binomial(4,k) * k^n.
%F A377399 G.f.: (1-14*x+83*x^2-262*x^3+384*x^4)/((1-x) * (1-2*x) * (1-3*x) * (1-4*x)).
%F A377399 a(n) = 4^n - 8*3^n + 3*2^(n+3) - 32 for n > 0. - _Stefano Spezia_, Oct 27 2024
%F A377399 a(0) = 1; a(n) = Sum_{k=1..n} (1 - 5 * k/n) * binomial(n,k) * a(n-k). - _Seiichi Manyama_, Oct 27 2024
%o A377399 (PARI) a(n) = sum(k=0, 4, (-1)^k*k!*binomial(4, k)*stirling(n, k, 2));
%o A377399 (PARI) a(n) = sum(k=0, 4, (-1)^k*2^(4-k)*binomial(4, k)*k^n);
%Y A377399 Cf. A226738.
%K A377399 sign,easy
%O A377399 0,2
%A A377399 _Seiichi Manyama_, Oct 27 2024