OFFSET
1,4
COMMENTS
Also the Bell transform of A338814.
LINKS
Seiichi Manyama, Rows n = 1..100, flattened
Peter Luschny, The Bell transform.
FORMULA
EXAMPLE
exp(Sum_{n>0} u*A048272(n)*x^n/n) = 1 + u*x + u^2*x^2/2! + (4*u+u^3)*x^3/3! + ... .
Triangle begins:
1;
0, 1;
4, 0, 1;
-6, 16, 0, 1;
48, -30, 40, 0, 1;
0, 448, -90, 80, 0, 1;
1440, -840, 2128, -210, 140, 0, 1;
-10080, 23532, -6720, 7168, -420, 224, 0, 1;
...
MATHEMATICA
a[n_] := a[n] = If[n == 0, 0, (n - 1)! * DivisorSum[n, (-1)^(# + 1) &]]; T[n_, k_] := T[n, k] = If[k == 0, Boole[n == 0], Sum[a[j] * Binomial[n - 1, j - 1] * T[n - j, k - 1], {j, 0, n - k + 1}]]; Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Amiram Eldar, Apr 28 2021 *)
PROG
(PARI) {T(n, k) = my(u='u); n!*polcoef(polcoef(prod(j=1, n, (1+x^j+x*O(x^n))^(u/j)), n), k)}
(PARI) a(n) = if(n<1, 0, (n-1)!*sumdiv(n, d, (-1)^(d+1)));
T(n, k) = if(k==0, 0^n, sum(j=0, n-k+1, binomial(n-1, j-1)*a(j)*T(n-j, k-1)))
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Nov 10 2020
STATUS
approved