A395559 1 = Sum_{n>=0} a(n) * x^n * (1 - (2*n+1)*x)^3.

1, 3, 24, 280, 4161, 74187, 1533088, 35893920, 936693681, 26911176067, 842965594392, 28564004820888, 1040256607904209, 40494874311730731, 1677141926085541632, 73603066948190278912, 3410716757745670379553, 166367131440489068335299, 8518446121149783644274136

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

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

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

Mathematica

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}]

Prog

(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)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A222080, A219779, A395560.

Sequence in context: A354289 A351763 A381595 * A355794 A384435 A355426

Adjacent sequences: A395554 A395557 A395558 * A395560 A395561 A395562

Keyword

nonn

Author

Vaclav Kotesovec, Apr 28 2026

Status

approved