A294373
Product of first n Bell numbers.
Original entry on oeis.org
1, 1, 2, 10, 150, 7800, 1583400, 1388641800, 5748977052000, 121573617718644000, 14099500314919737900000, 9567497928695086546803000000, 40313580569855830588349480391000000, 1114446238307803607782300144651734867000000
Offset: 0
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B:= map(combinat:-bell, [$0..19]):
map(i -> convert(B[1..i],`*`),[$1..20]); # Robert Israel, Oct 29 2017
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Table[Product[BellB[k], {k, 0, n}], {n, 0, 15}]
A342166
Product of first n Fubini numbers.
Original entry on oeis.org
1, 1, 3, 39, 2925, 1582425, 7410496275, 350464600333575, 191295845123076910125, 1355763582602823185129417625, 138623522325287867599380791765497875, 224935042709004795568466587349227029537282375, 6318777956744220129890735589019782971247629409914638125
Offset: 0
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g:= proc(n) option remember; `if`(n=0, 1,
add(g(n-j)*binomial(n, j), j=1..n))
end:
a:= proc(n) option remember; `if`(n=0, 1, a(n-1)*g(n)) end:
seq(a(n), n=0..15); # Alois P. Heinz, Mar 03 2021
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Table[Product[Sum[j!*StirlingS2[k, j], {j, 0, k}], {k, 1, n}], {n, 0, 12}]
Table[Product[PolyLog[-k, 1/2]/2, {k, 1, n}], {n, 0, 12}]
FoldList[Times, 1, Table[PolyLog[-n, 1/2]/2, {n, 1, 12}]]
A342177
Product of first n Motzkin numbers.
Original entry on oeis.org
1, 1, 2, 8, 72, 1512, 77112, 9793224, 3163211352, 2641281478920, 5779123875876960, 33507360232334614080, 519732664563742198994880, 21743016022024154894950804800, 2470745882646692817332839752643200, 767344490265348681664694707657903910400
Offset: 0
-
b:= proc(n) option remember; `if`(n<2, 1,
((2*n+1)*b(n-1) +(3*n-3)*b(n-2))/(n+2))
end:
a:= proc(n) a(n):=`if`(n=0, 1, a(n-1)*b(n)) end:
seq(a(n), n=0..18); # Alois P. Heinz, Mar 04 2021
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Table[Product[Hypergeometric2F1[(1-k)/2, -k/2, 2, 4], {k, 1, n}], {n, 0, 15}]
FoldList[Times, 1, Table[Hypergeometric2F1[(1 - n)/2, -n/2, 2, 4], {n, 1, 15}]]
A342178
Product of first n central Delannoy numbers.
Original entry on oeis.org
1, 3, 39, 2457, 788697, 1327377051, 11931792311439, 580350446236081521, 154215943727867706493809, 225550533306461376412704772467, 1826384842574005591817185497927226551, 82272644789290466599017454496002856892236169
Offset: 0
-
b:= proc(n) option remember; `if`(n<1, 1,
(3*(2*n-1)*b(n-1) -(n-1)*b(n-2))/n)
end:
a:= proc(n) a(n):=`if`(n=0, 1, a(n-1)*b(n)) end:
seq(a(n), n=0..15); # Alois P. Heinz, Mar 04 2021
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Table[Product[Hypergeometric2F1[-k, k+1, 1, -1], {k, 1, n}], {n, 0, 15}]
FoldList[Times, 1, Table[Hypergeometric2F1[-n, n + 1, 1, -1], {n, 1, 15}]]
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D(n) = sum(k=0, n, binomial(n, k)*binomial(n+k, k)); \\ A001850
a(n) = prod(k=0, n, D(k)); \\ Michel Marcus, Mar 04 2021
Showing 1-4 of 4 results.