This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A137478 #9 Sep 08 2022 08:45:32
%S A137478 1,1,1,2,4,1,6,18,9,1,30,120,90,20,1,240,1200,1200,400,40,1,3120,
%T A137478 18720,23400,10400,1560,78,1,65520,458640,687960,382200,76440,5733,
%U A137478 147,1,2227680,17821440,31187520,20791680,5197920,519792,19992,272,1
%N A137478 A triangle of recursive Fibonacci Lah numbers: f(n) = Fibonacci(n)*f(n - 1), L(n, k) = binomial(n-1, k-1)*(f(n)/f(k)).
%C A137478 Row sums are: {1, 2, 7, 34, 261, 3081, 57279, 1676641, 77766297, 5728225636, 671925730146, ...}.
%D A137478 Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), page86
%H A137478 G. C. Greubel, <a href="/A137478/b137478.txt">Rows n = 1..100 of triangle, flattened</a>
%F A137478 With f(n) = Fibonacci(n)*f(n-1) then the triangle is formed by L(n, k) = binomial(n-1, k-1)*(f(n)/f(k)).
%F A137478 With f(n) = Product_{j=1..n} Fibonacci(j) then the triangle is formed by T(n, k) = binomial(n-1, k-1)*(f(n)/f(k)). - _G. C. Greubel_, May 15 2019
%e A137478 Triangle begins as:
%e A137478 1;
%e A137478 1, 1;
%e A137478 2, 4, 1;
%e A137478 6, 18, 9, 1;
%e A137478 30, 120, 90, 20, 1;
%e A137478 240, 1200, 1200, 400, 40, 1;
%e A137478 3120, 18720, 23400, 10400, 1560, 78, 1;
%e A137478 65520, 458640, 687960, 382200, 76440, 5733, 147, 1;
%t A137478 f[n_]:= Product[Fibonacci[j], {j, 1, n}]; Table[Binomial[n-1, k-1]* f[n]/f[k], {n, 1, 12}, {k, 1, n}]//Flatten (* _G. C. Greubel_, May 15 2019 *)
%o A137478 (PARI)
%o A137478 {f(n) = prod(j=1,n, fibonacci(j))};
%o A137478 {T(n,k) = binomial(n-1, k-1)*(f(n)/f(k))};
%o A137478 for(n=1, 12, for(k=1, n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, May 15 2019
%o A137478 (Magma)
%o A137478 f:= func< n | (&*[Fibonacci(j): j in [1..n]]) >;
%o A137478 [[Binomial(n-1,k-1)*(f(n)/f(k)): k in [1..n]]: n in [1..12]]; // _G. C. Greubel_, May 15 2019
%o A137478 (Sage)
%o A137478 def f(n): return product(fibonacci(j) for j in (1..n))
%o A137478 [[binomial(n-1,k-1)*(f(n)/f(k)) for k in (1..n)] for n in (1..12)] # _G. C. Greubel_, May 15 2019
%Y A137478 Cf. A000045, A105278.
%K A137478 nonn,tabl
%O A137478 1,4
%A A137478 _Roger L. Bagula_, Apr 22 2008
%E A137478 Edited by _G. C. Greubel_, May 15 2019