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

0,2

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

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. A007318, A276085.

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

Sequence in context: A129340 A276588 A275951 * A280094 A025053 A140496

Adjacent sequences: A276583 A276584 A276585 * A276587 A276588 A276589

Keyword

nonn,tabl

Author

Antti Karttunen, Sep 18 2016

Status

approved