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!);
A375628
Expansion of e.g.f. exp(2*x^3) / (1 - x * exp(x^3)).
Original entry on oeis.org
1, 1, 2, 18, 96, 600, 5760, 57960, 645120, 8285760, 117936000, 1842825600, 31374604800, 578334556800, 11493004723200, 244720360684800, 5555523785011200, 134002274473267200, 3422904611167641600, 92290617116425728000, 2619214995575033856000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x^3)/(1-x*exp(x^3))))
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a(n) = n!*sum(k=0, n\3, (n-3*k+2)^k/k!);
A375654
Expansion of e.g.f. exp(2*x^2 + x * exp(x^2)).
Original entry on oeis.org
1, 1, 5, 19, 97, 641, 4021, 33475, 272609, 2559457, 25926661, 273419411, 3221437825, 38674360609, 506595820277, 6895149870211, 98785254688321, 1496456813264705, 23400554985371269, 386926938274889107, 6593495476334628641, 117506166655500705601
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x^2+x*exp(x^2))))
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a(n) = n!*sum(k=0, n\2, (n-2*k+2)^k/(k!*(n-2*k)!));
Showing 1-3 of 3 results.