A371309
Expansion of e.g.f. Product_{k>=1} (1 + x^k/k!)^(k^2).
Original entry on oeis.org
1, 1, 4, 21, 88, 645, 4386, 33061, 296808, 2674377, 26757190, 285294801, 3199971336, 38104015417, 476816609192, 6261875218215, 85736036949856, 1227373767823617, 18255004438680558, 281702101344334993, 4509097743074878200, 74606738071821274641, 1275212550939684334384
Offset: 0
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nmax = 22; CoefficientList[Series[Product[(1 + x^k/k!)^(k^2), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
A371482
Expansion of e.g.f. Product_{k>=1} (1 + x^k/k!)^(2^k).
Original entry on oeis.org
1, 2, 6, 32, 164, 1032, 7728, 59376, 522600, 4946768, 49680656, 540031296, 6195155744, 75183755584, 961596510272, 12909563309952, 181305865742240, 2657525771641664, 40594443765953472, 643987597483557888, 10601112599585001984, 180727870834447607808, 3185418524574895953152
Offset: 0
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nmax = 22; CoefficientList[Series[Product[(1 + x^k/k!)^(2^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
A371308
Expansion of e.g.f. Product_{k>=1} (1 + x^k/k!)^prime(k).
Original entry on oeis.org
1, 2, 5, 23, 101, 511, 3300, 20499, 147249, 1158047, 9284124, 82250155, 762408746, 7406758725, 75928931645, 815389826454, 9127145085135, 106002459387831, 1287304713397098, 16132127163478581, 209381715443456410, 2814011969429674997, 38957100435462040565
Offset: 0
-
nmax = 22; CoefficientList[Series[Product[(1 + x^k/k!)^Prime[k], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
A371480
Expansion of e.g.f. Product_{k>=1} (1 + x^k/k!)^(k-1).
Original entry on oeis.org
1, 0, 1, 2, 3, 24, 70, 300, 1365, 10136, 48636, 253560, 2069430, 13716780, 107972579, 695118606, 6155201325, 53001340112, 483401450344, 4129645998960, 36957700537146, 398523920633940, 3954961713704673, 42541112692428746, 430044528651402148
Offset: 0
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nmax = 24; CoefficientList[Series[Product[(1 + x^k/k!)^(k - 1), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
A371481
Expansion of e.g.f. Product_{k>=1} (1 + x^k/k!)^(k*(k+1)/2).
Original entry on oeis.org
1, 1, 3, 15, 52, 335, 2031, 12880, 102614, 802443, 6956995, 64721756, 633754320, 6551212057, 71375943289, 820250162880, 9747543483676, 121775559807881, 1580353806494781, 21246545374234378, 296590230821338520, 4280692741624646151, 63852747607056438283
Offset: 0
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nmax = 22; CoefficientList[Series[Product[(1 + x^k/k!)^(k (k + 1)/2), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
A371484
Expansion of e.g.f. Product_{k>=1} (1 + x^k/k!)^(2^(k-1)).
Original entry on oeis.org
1, 1, 2, 10, 30, 166, 968, 5440, 39112, 289096, 2330832, 19947280, 185603520, 1807683008, 18554569504, 203803276960, 2315043684112, 27640348895248, 344414508782624, 4483617418231456, 60518677509951520, 846362835642437536, 12289340439560875264
Offset: 0
-
nmax = 22; CoefficientList[Series[Product[(1 + x^k/k!)^(2^(k - 1)), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
Showing 1-6 of 6 results.
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