A369751
Expansion of e.g.f. exp(1 - (1+x)^3).
Original entry on oeis.org
1, -3, 3, 21, -63, -423, 1899, 15201, -72063, -832491, 3105459, 60090093, -110508543, -5224722831, -3828328677, 510699368313, 2104026859521, -52582823289171, -473592954347037, 5168227121231301, 92434892126557761, -357595962971807223, -17085974691782295477
Offset: 0
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A369751 := proc(n)
option remember ;
if n =0 then
1;
else
add( binomial(2,k-1) * procname(n-k)/(n-k)!,k=1..min(3,n)) ;
-3*(n-1)!*% ;
end if;
end proc:
seq(A369751(n),n=0..20) ; # R. J. Mathar, Feb 02 2024
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(1-(1+x)^3)))
A369753
Expansion of e.g.f. exp(1 - (1+x)^5).
Original entry on oeis.org
1, -5, 5, 115, -95, -8245, -21275, 896275, 8801825, -95466725, -2703832475, -3522650125, 717727962625, 9961465952875, -118944021914875, -5634631318806125, -37511809003469375, 2020875725751906875, 55489065505990733125, -65182838564153418125
Offset: 0
A369752
Expansion of e.g.f. exp(1 - (1+x)^4).
Original entry on oeis.org
1, -4, 4, 56, -104, -2464, 1696, 181184, 462016, -17069824, -141580544, 1593913856, 33015560704, -47193585664, -6973651011584, -50207289585664, 1214484253413376, 25500259291480064, -72069247145590784, -8696105637665603584, -81680899029758541824
Offset: 0
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With[{nn=20},CoefficientList[Series[Exp[1-(1+x)^4],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 29 2024 *)
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(1-(1+x)^4)))
A369754
a(n) = n! * [x^n] exp(1 - (1+x)^n).
Original entry on oeis.org
1, -1, 2, 21, -104, -8245, -124344, 7728581, 757142912, 21142327671, -3194024271200, -589138966169611, -38768504982354432, 4948651031184677219, 2022468386748039472256, 303711906641250589741125, -7986432746850744238505984, -19535207301291993249120303121
Offset: 0
Showing 1-4 of 4 results.