A370988
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*(exp(x) - 1)) ).
Original entry on oeis.org
1, 0, 2, 3, 76, 425, 10326, 119077, 3158968, 57929265, 1740086290, 44066266541, 1512768107940, 48660920528233, 1905202422005806, 73878129769929045, 3275941116578461936, 147981592692778718561, 7366814796135956094378, 378666415166758834858237
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x)-1)))/x))
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a(n) = sum(k=0, n\2, (n+k)!*stirling(n-k, k, 2)/(n-k)!)/(n+1);
A370994
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x^2*log(1-x)) ).
Original entry on oeis.org
1, 0, 0, 6, 12, 40, 3060, 23688, 191520, 9698400, 158548320, 2304973440, 100716073920, 2627516361600, 58513944513024, 2512156283683200, 89046056086041600, 2739316757454950400, 124170651534918297600, 5440968468533003212800, 215067442349096186572800
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x^2*log(1-x)))/x))
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a(n) = sum(k=0, n\3, (n+k)!*abs(stirling(n-2*k, k, 1))/(n-2*k)!)/(n+1);
A376345
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*(exp(x^2) - 1)) ).
Original entry on oeis.org
1, 0, 0, 6, 0, 60, 2880, 840, 201600, 7998480, 12700800, 1816547040, 67898476800, 311359688640, 35628798965760, 1317155266627200, 12924530383564800, 1308998905659244800, 49463008450023168000, 863080350836537433600, 81264621182097120768000, 3227330594664084337228800, 87828327888763088096870400
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x^2)-1)))/x))
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a(n) = sum(k=0, n\2, (2*n-2*k)!*stirling(k, n-2*k, 2)/k!)/(n+1);
A370990
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^3*(exp(x) - 1)) ).
Original entry on oeis.org
1, 0, 0, 0, 24, 60, 120, 210, 201936, 1996344, 12701520, 64865790, 17053788840, 374788816116, 4944496679304, 50034166184730, 6390396135006240, 239770550508132720, 5363062998193560096, 89908444484550625014, 7402557588108228698040
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^3*(exp(x)-1)))/x))
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a(n) = sum(k=0, n\4, (n+k)!*stirling(n-3*k, k, 2)/(n-3*k)!)/(n+1);
A371304
E.g.f. satisfies A(x) = 1/(1 - x^2*(exp(x*A(x)) - 1)).
Original entry on oeis.org
1, 0, 0, 6, 12, 20, 1470, 12642, 70616, 2131992, 39352410, 470186750, 11032124532, 295053244356, 5896487364950, 146264289411450, 4625791393554480, 130492119237611312, 3837833086814864946, 135471306780659593206, 4800394977109827314060
Offset: 0
-
a(n) = n!*sum(k=0, n\3, (n-k)!*stirling(n-2*k, k, 2)/((n-2*k)!*(n-2*k+1)!));
Showing 1-5 of 5 results.