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A276586
Square array A(row,col) = Sum_{k=0..row} binomial(row,k)*A002110(col+k), read by descending antidiagonals as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...
6
1, 2, 3, 6, 8, 11, 30, 36, 44, 55, 210, 240, 276, 320, 375, 2310, 2520, 2760, 3036, 3356, 3731, 30030, 32340, 34860, 37620, 40656, 44012, 47743, 510510, 540540, 572880, 607740, 645360, 686016, 730028, 777771, 9699690, 10210200, 10750740, 11323620, 11931360, 12576720, 13262736, 13992764, 14770535
OFFSET
0,2
FORMULA
A(row,col) = Sum_{k=0..row} binomial(row,k)*A002110(col+k).
A(row,col) = A276085(A066117(row+1,col+1)).
EXAMPLE
The top left corner of the array:
1, 2, 6, 30, 210, 2310, 30030
3, 8, 36, 240, 2520, 32340, 540540
11, 44, 276, 2760, 34860, 572880, 10750740
55, 320, 3036, 37620, 607740, 11323620, 253753500
375, 3356, 40656, 645360, 11931360, 265077120, 7422334920
3731, 44012, 686016, 12576720, 277008480, 7687412040, 235239464460
MATHEMATICA
primorial[n_] := Product[Prime[k], {k, 1, n}]; A[n_, k_] := Sum[Binomial[n, j]*primorial[k+j], {j, 0, n}]; Table[A[n-k, k], {n, 0, 9}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Jan 22 2017 *)
PROG
(Scheme)
(define (A276586 n) (A276586bi (A002262 n) (A025581 n)))
(define (A276586bi row col) (A276085 (A066117bi (+ 1 row) (+ 1 col))))
(PARI) P(n)=prod(i=1, n, prime(i));
T(n, k) = sum(j=0, n, binomial(n, j)*P(k + j));
for(n=0, 10, for(k=0, n, print1(T(k, n - k), ", "); ); print(); ) \\ Indranil Ghosh, Apr 11 2017
CROSSREFS
Transpose: A276587.
Topmost row: A002110, Leftmost column: A136104.
Cf. also arrays A066117, A276588, A099884, A255483.
Sequence in context: A129340 A276588 A275951 * A280094 A025053 A140496
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Sep 18 2016
STATUS
approved