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), ...

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

Author

Antti Karttunen, Sep 18 2016

Keywords

• nonn
• tabl

Examples

			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
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..989; the first 44 antidiagonals of array
• Index entries for triangles and arrays related to Pascal's triangle
• Index entries for sequences related to primorial numbers

Crossrefs

Transpose: A276587.

Topmost row: A002110, Leftmost column: A136104.

Cf. A007318, A276085.

Cf. also arrays A066117, A276588, A099884, A255483.

Programs

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 *)

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

Scheme

(define (A276586 n) (A276586bi (A002262 n) (A025581 n)))
(define (A276586bi row col) (A276085 (A066117bi (+ 1 row) (+ 1 col))))

Formula

A(row,col) = Sum_{k=0..row} binomial(row,k)*A002110(col+k).

A(row,col) = A276085(A066117(row+1,col+1)).