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A330045 Expansion of e.g.f. exp(x) / (1 - x^4). 9
1, 1, 1, 1, 25, 121, 361, 841, 42001, 365905, 1819441, 6660721, 498971881, 6278929801, 43710250585, 218205219961, 21795091762081, 358652470233121, 3210080802962401, 20298322381652065, 2534333270094778681, 51516840824285500441, 563561785768079119561 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
FORMULA
G.f.: Sum_{k>=0} (4*k)! * x^(4*k) / (1 - x)^(4*k + 1).
a(0) = a(1) = a(2) = a(3) = 1; a(n) = n*(n - 1)*(n - 2)*(n - 3)*a(n - 4) + 1.
a(n) = Sum_{k=0..floor(n/4)} n! / (n - 4*k)!.
a(n) ~ n! * (2*cos(Pi*n/2 - 1) + exp(1) + (-1)^n*exp(-1))/4. - Vaclav Kotesovec, Apr 18 2020
MATHEMATICA
nmax = 22; CoefficientList[Series[Exp[x]/(1 - x^4), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[n!/(n - 4 k)!, {k, 0, Floor[n/4]}], {n, 0, 22}]
CROSSREFS
Outer diagonal of A158777.
Sequence in context: A361637 A190875 A205800 * A362349 A274783 A354553
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 28 2019
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)