A143968
Denominators of numbers with g.f. exp(1-(1-x)^(1/2)).
Original entry on oeis.org
1, 2, 4, 48, 384, 1920, 46080, 645120, 5160960, 185794560, 530841600, 40874803200, 280284364800, 51011754393600, 714164561510400, 42849873690624000, 1371195958099968000, 302731575164928000, 1678343852714360832000, 100120983364435968000, 1275541328062914232320000
Offset: 0
1, 1/2, 1/4, 7/48, 37/384, 133/1920, 2431/46080, 27007/645120, 176761/5160960, ...
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S:= series(exp(1-(1-x)^(1/2)),x,21):
seq(denom(coeff(S,x,i)),i=0..20); # Robert Israel, Mar 23 2023
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CoefficientList[Series[Exp[1-Sqrt[1-x]],{x,0,20}],x]//Denominator (* Harvey P. Dale, Sep 13 2019 *)
A144525
Numerators of expansion of exp(1-sqrt(1-3*x)).
Original entry on oeis.org
1, 3, 9, 63, 999, 10773, 196911, 6562701, 128858769, 1295150391, 9472912497, 1895674219911, 11402464056957, 5518764184829697, 207312834548907783, 11211449358195509373, 976639971170302762149, 590444288071830626391, 1001189263964851383868503
Offset: 0
1 + (3/2)*x + (9/4)*x^2 + (63/16)*x^3 + (999/128)*x^4 + (10773/640)*x^5 + (196911/5120)*x^6 + ...
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CoefficientList[Series[Exp[1-Sqrt[1-3x]],{x,0,20}],x]//Numerator (* Harvey P. Dale, Dec 27 2022 *)
A144526
Denominators of expansion of exp(1-sqrt(1-3*x)).
Original entry on oeis.org
1, 2, 4, 16, 128, 640, 5120, 71680, 573440, 2293760, 6553600, 504627200, 1153433600, 209924915200, 2938948812800, 58778976256000, 1880927240192000, 415269650432000, 255806104666112000, 15260018802688000, 194412639546245120000, 418734915945758720000
Offset: 0
1 + (3/2)*x + (9/4)*x^2 + (63/16)*x^3 + (999/128)*x^4 + (10773/640)*x^5 + (196911/5120)*x^6 + ...
A381845
a(n) = denominator( (e/Pi)*Integral_{x=-oo..+oo} cos(x)/(1 + x^2)^n dx ).
Original entry on oeis.org
1, 1, 8, 48, 192, 3840, 46080, 322560, 10321920, 26542080, 1857945600, 11678515200, 1961990553600, 25505877196800, 1428329123020800, 42849873690624000, 8903869857792000, 46620662575398912000, 2634762720116736000, 31888533201572855808000, 196237127394294497280000
Offset: 1
1, 1, 7/8, 37/48, 133/192, 2431/3840, 27007/46080, 176761/322560, ...
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a[n_]:=Denominator[(E/Pi)Integrate[Cos[x]/(1 + x^2)^n,{x,-Infinity,Infinity}]]; Array[a,21]
Showing 1-4 of 4 results.