A375604
Expansion of e.g.f. 1 / (exp(-x^2) - x).
Original entry on oeis.org
1, 1, 4, 18, 108, 840, 7680, 82320, 1009680, 13910400, 213071040, 3589850880, 65975152320, 1313624632320, 28166959941120, 647099547494400, 15857424488505600, 412878579034521600, 11382450106662835200, 331230511848421785600, 10146149192841050188800
Offset: 0
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With[{nn=20},CoefficientList[Series[1/(Exp[-x^2]-x),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 01 2025 *)
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(exp(-x^2)-x)))
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a(n) = n!*sum(k=0, n\2, (n-2*k+1)^k/k!);
A375633
Expansion of e.g.f. exp(x^2) / (1 - x * exp(x^2/2)).
Original entry on oeis.org
1, 1, 4, 15, 84, 555, 4440, 41265, 438480, 5240025, 69582240, 1016350335, 16194911040, 279560396115, 5197054262400, 103514720133825, 2199255573715200, 49645309340451825, 1186599954328588800, 29937224154635772975, 795051251297099596800
Offset: 0
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A375633 := proc(n)
n!*add(((n-2*k+2)/2)^k/k!,k=0..floor(n/2)) ;
end proc:
seq(A375633(n),n=0..60) ; # R. J. Mathar, Aug 23 2024
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^2)/(1-x*exp(x^2/2))))
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a(n) = n!*sum(k=0, n\2, ((n-2*k+2)/2)^k/k!);
A375395
Expansion of e.g.f. 1 / (exp(-x^3/6) - x).
Original entry on oeis.org
1, 1, 2, 7, 32, 180, 1210, 9520, 85680, 867160, 9749600, 120582000, 1626994600, 23782158400, 374367193200, 6314037129400, 113591474796800, 2171267969270400, 43944509528920000, 938808209417478400, 21111813400597920000, 498498097342637392000
Offset: 0
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A375395 := proc(n)
n!*add(((n-3*k+1)/6)^k/k!,k=0..floor(n/3)) ;
end proc:
seq(A375395(n),n=0..60) ; # R. J. Mathar, Aug 23 2024
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(exp(-x^3/6)-x)))
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a(n) = n!*sum(k=0, n\3, ((n-3*k+1)/6)^k/k!);
A375608
Expansion of e.g.f. 1 / (exp(x^2) - x).
Original entry on oeis.org
1, 1, 0, -6, -36, -120, 240, 8400, 82320, 362880, -3507840, -103783680, -1268688960, -4843238400, 175429013760, 5052189542400, 68016191443200, 55329155481600, -23284682272051200, -668640423164313600, -9013925405784499200, 57340797108269875200
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(exp(x^2)-x)))
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a(n) = n!*sum(k=0, n\2, (-n+2*k-1)^k/k!);
Showing 1-4 of 4 results.