A375664
Expansion of e.g.f. 1 / (1 - x * (exp(x^2) - 1))^2.
Original entry on oeis.org
1, 0, 0, 12, 0, 120, 2160, 1680, 120960, 1481760, 6350400, 240166080, 2754259200, 31152401280, 894303970560, 11769588230400, 228232766361600, 5845147711603200, 98290727395660800, 2502848611354291200, 63417766359467520000, 1376904298716724377600
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-x*exp(x^2))^2))
-
a(n) = n!*sum(k=0, n\2, (n-2*k+1)!*stirling(k, n-2*k, 2)/k!);
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
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-x*exp(x^2))^3))
-
a(n) = n!*sum(k=0, n\2, (n-2*k+2)!*stirling(k, n-2*k, 2)/k!)/2;
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
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x^2)-1)))/x))
-
a(n) = sum(k=0, n\2, (2*n-2*k)!*stirling(k, n-2*k, 2)/k!)/(n+1);
A375589
Expansion of e.g.f. 1 / (1 + x - x * exp(x^3)).
Original entry on oeis.org
1, 0, 0, 0, 24, 0, 0, 2520, 40320, 0, 604800, 39916800, 479001600, 259459200, 50854003200, 1961511552000, 21097146470400, 88921857024000, 8002967132160000, 243459152346009600, 2642401903325184000, 38318206628782080000, 2435557926202232832000
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-x*exp(x^3))))
-
a(n) = n!*sum(k=0, n\3, (n-3*k)!*stirling(k, n-3*k, 2)/k!);
Showing 1-4 of 4 results.