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A370369
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a(n) = n! + Sum_{k=1..n-1} (n-k)*k! = n! + A014145(n-1); for n >= 2, number of m such that any two consecutive digits of the base-n expansion of m differ by 1 after arranging the digits in decreasing order.
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1
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1, 3, 10, 37, 166, 919, 6112, 47305, 416098, 4091131, 44417044, 527456557, 6798432070, 94499679583, 1408924024696, 22425642181009, 379514672913322, 6804212771165635, 128827325000617948, 2568509718703606261, 53787877376348226574, 1180349932648067726887, 27086018941198865627200
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OFFSET
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1,2
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COMMENTS
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Given n, the largest such number is Sum_{i=0..n-1} i*n^i = A062813(n). If zero is excluded, the number of such k with d digits in base n, 1 <= d <= n, is (n+1-d)*d! - (d-1)!.
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LINKS
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EXAMPLE
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a(3) = 10 because such numbers are 0_3, 1_3, 2_3, 10_3, 12_3, 21_3, 102_3, 120_3, 201_3 and 210_3.
a(10) = 4091131 is the number of terms of A215014.
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PROG
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(PARI) a(n) = n! + sum(k=1, n-1, (n-k)*k!)
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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