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

0,3

Comments

Conjecture: in this sequence only two semiprimes (4,25).

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = A000110(n)*A004098(n).

Example

a(4) = 765 because Bell(4) = 15 and 15*51 = 765.
s(5) = 1300 because Bell(5) = 52 and 52*25 = 1300.

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 *)

Prog

(Magma) [Bell(n)*Seqint(Reverse(Intseq(Bell(n)))): n in [0..30]];
(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

Crossrefs

Cf. A000110, A004098, A133019, A133022.

Sequence in context: A123129 A075577 A004019 * A277110 A072882 A014253

Adjacent sequences: A302089 A302090 A302091 * A302093 A302094 A302095

Keyword

nonn,base,easy

Author

Vincenzo Librandi, Apr 01 2018

Status

approved