A377833
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^3 * exp(-x) ).
Original entry on oeis.org
1, 4, 51, 1174, 39833, 1799136, 101821723, 6938396368, 553482404721, 50619262481920, 5223014483031491, 600332651141435136, 76075005337204547209, 10538051760153093320704, 1584264031801742560408875, 256912816791069951740348416, 44703731640012047610981808097
Offset: 0
A377810
E.g.f. satisfies A(x) = exp(x * A(x)) / (1 - x)^2.
Original entry on oeis.org
1, 3, 17, 154, 1993, 34066, 728209, 18733926, 564117425, 19473863986, 758421401401, 32901791851006, 1573602042306265, 82267318018246986, 4667656830688700801, 285662368622361581206, 18758565855176593500385, 1315663025587514658845026, 98160436697525045768511721
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x)^2))/(1-x)^2))
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a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(n+k+1, n-k)/k!);
A377828
E.g.f. satisfies A(x) = (1 + x)^3 * exp(x * A(x)).
Original entry on oeis.org
1, 4, 21, 193, 2669, 48711, 1113325, 30615019, 984983193, 36319515355, 1510538562641, 69968975169567, 3572684914283941, 199389519518767111, 12075888110164192917, 788850329621989132771, 55289606764547108653361, 4138807268239824817387443, 329564746571982961088975257
Offset: 0
A377599
E.g.f. satisfies A(x) = exp( x * A(x) / (1-x)^2 ) / (1-x).
Original entry on oeis.org
1, 2, 13, 145, 2277, 46461, 1172713, 35374697, 1243296169, 49940748073, 2258238723021, 113567169318285, 6289161888870061, 380364426242671469, 24948313525570134001, 1764095427822803465521, 133782341347522663175889, 10832097536377585282160337, 932693691617428946786304661
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x)^3))/(1-x)))
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a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(n+2*k, n-k)/k!);
A377608
E.g.f. satisfies A(x) = exp( x * A(x) / (1-x) ) / (1-x)^2.
Original entry on oeis.org
1, 3, 19, 202, 3085, 61886, 1544029, 46182900, 1612759369, 64455582394, 2902794546961, 145497909334856, 8035136800888333, 484821204654219798, 31735810390729211173, 2240132583683741633116, 169624462686462529305745, 13715713402047448280358002, 1179576532854283015832748697
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x)^3))/(1-x)^2))
-
a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(n+2*k+1, n-k)/k!);
Showing 1-5 of 5 results.