A358264
Expansion of e.g.f. 1/(1 - x * exp(x^2/2)).
Original entry on oeis.org
1, 1, 2, 9, 48, 315, 2520, 23415, 248640, 2972025, 39463200, 576413145, 9184855680, 158550787395, 2947473809280, 58707685211175, 1247293022976000, 28156003910859825, 672972205556851200, 16978695795089253225, 450907982644863744000, 12573634144960773960075
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(x^2/2))))
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a(n) = n!*sum(k=0, n\2, (n-2*k)^k/(2^k*k!));
A370931
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*exp(x^3/6)) ).
Original entry on oeis.org
1, 1, 4, 30, 340, 5180, 99360, 2300830, 62473600, 1946941920, 68507714800, 2686816932800, 116225776497600, 5497681373384200, 282305750023897600, 15640212734095950000, 929908726447266966400, 59061538103044360083200, 3990922849835432102592000
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*exp(x^3/6)))/x))
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a(n) = sum(k=0, n\3, (n-3*k)^k*(2*n-3*k)!/(6^k*k!*(n-3*k)!))/(n+1);
A375634
Expansion of e.g.f. exp(x^3) / (1 - x * exp(x^3/6)).
Original entry on oeis.org
1, 1, 2, 12, 52, 280, 2160, 16870, 150080, 1557360, 17491600, 215908000, 2923905600, 42734091400, 672515043200, 11347480544400, 204142655516800, 3902009862150400, 78976503077472000, 1687212801048174400, 37941749192547200000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^3)/(1-x*exp(x^3/6))))
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a(n) = n!*sum(k=0, n\3, ((n-3*k+6)/6)^k/k!);
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