A371621 Expansion of e.g.f. 1 / (1 - x + x^2/2 - x^3/3 + x^4/4).

1, 1, 1, 2, 4, -10, -130, -840, -5880, -36960, -142800, 184800, 12843600, 229429200, 3035432400, 31615584000, 258306048000, 943422480000, -26673126480000, -902769547680000, -18345450483360000, -300501672831360000, -3983084426280960000

Offset

0,4

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = n * a(n-1) - n * (n-1) * a(n-2) / 2 + n * (n-1) * (n-2) * a(n-3) / 3 - n * (n-1) * (n-2) * (n-3) * a(n-4) / 4.

Mathematica

nmax = 22; CoefficientList[Series[1/(1 - x + x^2/2 - x^3/3 + x^4/4), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = a[1] = a[2] = 1; a[3] = 2; a[n_] := a[n] = n a[n - 1] - n (n - 1) a[n - 2]/2 + n (n - 1) (n - 2) a[n - 3]/3 - n (n - 1) (n - 2) (n - 3) a[n - 4]/4; Table[a[n], {n, 0, 22}]

Crossrefs

Cf. A006252, A009775, A217260, A355294, A371605.

Sequence in context: A126140 A326967 A223851 * A297364 A355203 A327059

Adjacent sequences: A371617 A371619 A371620 * A371622 A371623 A371624

Keyword

sign

Author

Ilya Gutkovskiy, Apr 01 2024

Status

approved