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A353822
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Product_{n>=1} (1 + x^n/n!)^a(n) = exp(-x)/(1 - x).
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3
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0, 1, 2, 9, 24, 110, 720, 5985, 39200, 343224, 3628800, 41295870, 479001600, 6130959120, 87104969952, 1318070979225, 20922789888000, 354344089779680, 6402373705728000, 121882240625961816, 2432849766865689600, 51041049953430700800, 1124000727777607680000
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OFFSET
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1,3
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LINKS
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MATHEMATICA
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nn = 23; f[x_] := Product[(1 + x^n/n!)^a[n], {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - Exp[-x]/(1 - x), {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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