A302092 Product of n-th Bell number and n-th Bell number written backwards.
1, 1, 4, 25, 765, 1300, 61306, 682306, 1713960, 1567246464, 67208788225, 51487177320, 33511259427028, 2030336608089664, 42761083701194302, 7549007599307190895, 776831192562116876947, 3388911887796350381712, 649070202541887765091474, 43774861324581222789850945
Offset: 0
Examples
a(4) = 765 because Bell(4) = 15 and 15*51 = 765. s(5) = 1300 because Bell(5) = 52 and 52*25 = 1300.
Programs
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Magma
[Bell(n)*Seqint(Reverse(Intseq(Bell(n)))): n in [0..30]];
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Maple
b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*binomial(n-1, j-1), j=1..n)) end: a:= n-> b(n)*(s-> parse(cat(seq(s[-i], i=1..length(s)))))(""||(b(n))): seq(a(n), n=0..25); # Alois P. Heinz, Apr 26 2018 -
Mathematica
BellB[#] FromDigits[Reverse[IntegerDigits[BellB[#]]]]&/@Range[0, 50] # IntegerReverse[#]&/@BellB[Range[0,20]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 29 2019 *)
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Perl
use ntheory ":all"; sub Bell {vecsum(map{stirling($[0],$,2)} 0..$[0])} for (0..30) { my $b=Bell($); print "$ ",vecprod($b,scalar(reverse($b))),"\n" } # _Dana Jacobsen, Mar 04 2019
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