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A358500
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a(n) = Sum_{k=0..floor(n/5)} (n-5*k)!.
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5
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1, 1, 2, 6, 24, 121, 721, 5042, 40326, 362904, 3628921, 39917521, 479006642, 6227061126, 87178654104, 1307677996921, 20922829805521, 355687907102642, 6402379932789126, 121645187587486104, 2432903315854636921, 51090963094539245521, 1124001083465514782642
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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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a(n) = n * a(n-1) + a(n-5) - n * a(n-6) for n > 5.
a(n) ~ n! * (1 + 1/n^5 + 10/n^6 + 65/n^7 + 350/n^8 + 1701/n^9 + 7771/n^10 + 34150/n^11 + 146905/n^12 + ...), the coefficients are Sum_{j=0..(k-4)/5} Stirling2(k,5*j+4). - Vaclav Kotesovec, Nov 24 2022
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PROG
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(PARI) a(n) = sum(k=0, n\5, (n-5*k)!);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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