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A348014 Triangle, read by rows, with row n forming the coefficients in Product_{k=0..n} (1 + k^k*x). 1
1, 1, 1, 1, 5, 4, 1, 32, 139, 108, 1, 288, 8331, 35692, 27648, 1, 3413, 908331, 26070067, 111565148, 86400000, 1, 50069, 160145259, 42405161203, 1216436611100, 5205269945088, 4031078400000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
Seiichi Manyama, Rows n = 0..37, flattened
FORMULA
T(0,0) = 1; T(n,k) = T(n-1,k) + n^n * T(n-1,k-1).
EXAMPLE
Triangle begins:
1;
1, 1;
1, 5, 4;
1, 32, 139, 108;
1, 288, 8331, 35692, 27648;
1, 3413, 908331, 26070067, 111565148, 86400000;
PROG
(PARI) T(n, k) = if(k==0, 1, if(k==n, prod(j=1, n, j^j), T(n-1, k)+n^n*T(n-1, k-1)));
(PARI) row(n) = Vecrev(prod(k=1, n, 1+k^k*x));
CROSSREFS
Column k=1 gives A001923.
The diagonal of the triangle is A002109.
Sequence in context: A182824 A329120 A152862 * A108440 A102220 A279151
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Sep 24 2021
STATUS
approved

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Last modified April 12 06:13 EDT 2024. Contains 371623 sequences. (Running on oeis4.)