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A371621
Expansion of e.g.f. 1 / (1 - x + x^2/2 - x^3/3 + x^4/4).
1
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
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
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Apr 01 2024
STATUS
approved