A375665
Expansion of e.g.f. 1 / (1 - x * (exp(x^2) - 1))^3.
Original entry on oeis.org
1, 0, 0, 18, 0, 180, 4320, 2520, 241920, 3674160, 12700800, 599749920, 7903526400, 77863705920, 2660390853120, 37269497865600, 683129089843200, 19948163057222400, 339567800885913600, 8690022866119795200, 241333983478748160000, 5217670959100125926400
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-x*exp(x^2))^3))
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a(n) = n!*sum(k=0, n\2, (n-2*k+2)!*stirling(k, n-2*k, 2)/k!)/2;
A375680
Expansion of e.g.f. 1 / (1 + x * log(1 - x^2))^2.
Original entry on oeis.org
1, 0, 0, 12, 0, 120, 2160, 3360, 120960, 1632960, 9979200, 255467520, 3592512000, 45664819200, 1070840010240, 18027225216000, 340344048844800, 8174882722406400, 169308486085939200, 4019018956285132800, 104511967278630912000, 2606273308503760896000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x^2))^2))
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a(n) = n!*sum(k=0, n\2, (n-2*k+1)!*abs(stirling(k, n-2*k, 1))/k!);
A375810
Expansion of e.g.f. 1/(1 - (exp(x^2) - 1)/x)^2.
Original entry on oeis.org
1, 2, 6, 30, 192, 1480, 13500, 141540, 1676640, 22141728, 322388640, 5130084960, 88561408320, 1648294876800, 32898981155040, 700940855815200, 15877318955097600, 380996919471168000, 9654670629548904960, 257627854786123261440, 7220676423560766566400
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(exp(x^2)-1)/x)^2))
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a(n) = n!*sum(k=0, n\2, (n-2*k+1)!*stirling(n-k, n-2*k, 2)/(n-k)!);
A376443
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*(exp(x^2) - 1))^2 ).
Original entry on oeis.org
1, 0, 0, 12, 0, 120, 10800, 1680, 766080, 55913760, 48686400, 12973625280, 878369184000, 2257312337280, 475877474392320, 31178226637958400, 176135891323392000, 32566007822802854400, 2111180034178805990400, 22027962609483730099200, 3749400628293386626560000, 244391453278125083388057600
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x^2)-1))^2)/x))
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a(n) = 2*n!*sum(k=0, n\2, (3*n-2*k+1)!*stirling(k, n-2*k, 2)/k!)/(2*n+2)!;
Showing 1-4 of 4 results.