A395559 - OEIS

A395559

1 = Sum_{n>=0} a(n) * x^n * (1 - (2*n+1)*x)^3.

%I #8 May 11 2026 07:19:20

%S 1,3,24,280,4161,74187,1533088,35893920,936693681,26911176067,

%T 842965594392,28564004820888,1040256607904209,40494874311730731,

%U 1677141926085541632,73603066948190278912,3410716757745670379553,166367131440489068335299,8518446121149783644274136

%N 1 = Sum_{n>=0} a(n) * x^n * (1 - (2*n+1)*x)^3.

%F a(n) = 3*(2*n - 1)*a(n-1) - 3*(2*n - 3)^2*a(n-2) + (2*n - 5)^3*a(n-3).

%F a(n) ~ 2^n * exp(2*sqrt(3*n) - n) * n^(n - 7/12) * (1 + 7/(48*sqrt(3*n))), where c = 0.11981699300544279084077765785418589242344890231573931622... - _Vaclav Kotesovec_, May 11 2026

%t RecurrenceTable[{-(2*n-5)^3*a[n-3] + 3*(2*n-3)^2*a[n-2] - 3*(2*n-1)*a[n-1] + a[n] == 0, a[1]==3, a[2]==24, a[3]==280}, a, {n, 0, 20}]

%o (PARI) {a(n)=polcoeff(1-sum(m=0, n-1, a(m)*x^m*(1-(2*m+1)*x+x*O(x^n))^3), n)}

%o for(n=0, 25, print1(a(n), ", "))

%Y Cf. A222080, A219779, A395560.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Apr 28 2026