A367880
Expansion of e.g.f. 1/(1 - 2 * x * (exp(x) - 1)).
Original entry on oeis.org
1, 0, 4, 6, 104, 490, 7452, 65534, 1062224, 13825746, 252414020, 4303920742, 89701635960, 1870259792570, 44391086228972, 1085906907998670, 29112549152845472, 813723252665063842, 24402507959486170260, 765358519469125339190
Offset: 0
-
a(n) = n!*sum(k=0, n\2, 2^k*k!*stirling(n-k, k, 2)/(n-k)!);
A375683
Expansion of e.g.f. 1 / (1 + x * (exp(x) - 1)).
Original entry on oeis.org
1, 0, -2, -3, 20, 115, -306, -6307, -6616, 462663, 2956130, -38945951, -656504388, 2325876683, 145820995670, 562691968005, -33452317341616, -449954883966065, 7055017491780810, 233802046526955497, -571834988279277340, -112474674691684827501
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*(exp(x)-1))))
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a(n) = n!*sum(k=0, n\2, (-1)^k*k!*stirling(n-k, k, 2)/(n-k)!);
A375696
Expansion of e.g.f. 1 / (1 - 3 * x * (exp(x) - 1))^(1/3).
Original entry on oeis.org
1, 0, 2, 3, 52, 245, 4206, 37807, 712552, 9755433, 207915490, 3830073731, 92948571420, 2139142283005, 58945940093782, 1617324856023255, 50252559901690576, 1593701025177559121, 55366628370374688714, 1986560560083994301611
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*x*(exp(x)-1))^(1/3)))
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a(n) = n!*sum(k=0, n\2, prod(j=0, k-1, 3*j+1)*stirling(n-k, k, 2)/(n-k)!);
A375697
Expansion of e.g.f. 1 / (1 - 3 * x * (exp(x) - 1))^(2/3).
Original entry on oeis.org
1, 0, 4, 6, 128, 610, 11712, 107114, 2167776, 30285378, 678296720, 12761459722, 321364284144, 7550564959106, 214210299545088, 5993932335381930, 190756625697021632, 6161493279498219394, 218469987108304908336, 7972839360644407925258
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*x*(exp(x)-1))^(2/3)))
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a(n) = n!*sum(k=0, n\2, prod(j=0, k-1, 3*j+2)*stirling(n-k, k, 2)/(n-k)!);
Showing 1-4 of 4 results.