A033647 Base 10 digital convolution sequence.

1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 40320, 403200, 846720, 2943360, 12620160, 66044160, 408885120, 2928240000, 23834805120, 217441486080, 47669610240, 482552582400, 1060444385280, 4146438320640, 18706642053120, 101826086906880, 648369805547520

Offset: 0

Author

David W. Wilson

Keywords

• base
• nonn

Examples

			Suppose base = 3 and a(0)..a(13) are 1 1 2 1 3 7 6 20 52 6 26 104 32 162. In base 3, 14 = 112, so we convolve the last three terms with 1, 1, 2 to obtain 104*1+32*1+162*2 = 460.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A033639, A033640, A033641, A033642, A033643, A033644, A033645, A033646.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, (l->
      add(l[i]*a(n-i), i=1..nops(l)))(convert(n, base, 10)))
    end:
seq(a(n), n=0..33);  # Alois P. Heinz, Apr 14 2021