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A222059
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a(n) = n-th harmonic-exponential number, multiplied by n!.
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2
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0, 1, 5, 44, 590, 11094, 276924, 8821056, 347992560, 16608856176, 941180477760, 62356907861280, 4768658639919360, 416372600735314560, 41123273761815517440, 4557176483095745510400, 562635159090115071744000, 76906191809174747446425600, 11573912988161070649533849600
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OFFSET
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0,3
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LINKS
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FORMULA
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Sum_{n>=0} a(n) * x^n / n!^2 = Sum_{n>=1} H(n) * (exp(x) - 1)^n / n!, where H(n) is the n-th harmonic number. - Ilya Gutkovskiy, Jun 03 2022
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MATHEMATICA
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Table[Sum[HarmonicNumber[k] StirlingS2[n, k] n!, {k, 0, n}], {n, 0, 20}] (* Vladimir Reshetnikov, Oct 20 2015 *)
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PROG
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(PARI) a(n) = sum(k=0, n, (sum(i=0, k, (-1)^i*binomial(k, i)*i^n) * (-1)^k/k!)*sum(i=1, k, 1/i) * n!); \\ Michel Marcus, Feb 08 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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