A319175
a(n) = n! * [x^n] Product_{k>=1} (1 + x^k/k!)^n.
Original entry on oeis.org
1, 1, 4, 36, 416, 6000, 106542, 2242093, 54399424, 1495318752, 45938780750, 1559858659359, 58007497143180, 2344682328265823, 102352889947823998, 4798930456964580045, 240518006611511552896, 12832137350594892322464, 726108032647676403262710, 43434461707962856186584307
Offset: 0
-
Table[n! SeriesCoefficient[Product[(1 + x^k/k!)^n, {k, 1, n}], {x, 0, n}], {n, 0, 19}]
Table[n! SeriesCoefficient[Exp[n Sum[Sum[(-1)^(k + 1) x^(j k)/(k (j!)^k), {j, 1, n}], {k, 1, n}]], {x, 0, n}], {n, 0, 19}]
A371312
Expansion of e.g.f. Product_{k>=1} 1 / (1 - x^k/k!)^2.
Original entry on oeis.org
1, 2, 8, 38, 228, 1562, 12386, 109286, 1073988, 11545994, 135393438, 1714890806, 23380747506, 341014477390, 5303722839850, 87582446980418, 1531259993710468, 28254163132485930, 548854481037814382, 11196310379931318758, 239346426732701009838, 5350768890908294837294
Offset: 0
-
nmax = 21; CoefficientList[Series[Product[1/(1 - x^k/k!)^2, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
A371389
Expansion of e.g.f. Product_{k>=1} (1 + x^k/k)^2.
Original entry on oeis.org
1, 2, 4, 16, 74, 388, 2756, 20872, 180008, 1758672, 18937152, 221914944, 2832193008, 39039810912, 575502635808, 9100950684480, 152818028328960, 2717564023296000, 51129136369981440, 1012979833297735680, 21074454817487953920, 460035753479203184640
Offset: 0
-
nmax = 21; CoefficientList[Series[Product[(1 + x^k/k)^2, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
A371551
Expansion of e.g.f. Product_{k>=1} (1 - x^k/k!)^2.
Original entry on oeis.org
1, -2, 0, 10, -4, -42, -258, 306, 5980, 3142, 61730, -794334, -3299074, -8459830, 40220390, 1550926110, 1631691740, 43693916390, -125593997262, -4079362135854, -32054212967294, -33715330874838, -600410923342450, 9383532800084966, 329821022627776798
Offset: 0
-
nmax = 24; CoefficientList[Series[Product[(1 - x^k/k!)^2, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
Showing 1-4 of 4 results.
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