A275950 Square array A(1,k) = A265905(k), A(n>1,k) = A(n-1, k+1) - A(n-1, k); successive differences of A265905 read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

1, 3, 2, 11, 8, 6, 49, 38, 30, 24, 291, 242, 204, 174, 150, 1979, 1688, 1446, 1242, 1068, 918, 15217, 13238, 11550, 10104, 8862, 7794, 6876, 136659, 121442, 108204, 96654, 86550, 77688, 69894, 63018, 1349627, 1212968, 1091526, 983322, 886668, 800118, 722430, 652536, 589518, 14561425, 13211798, 11998830, 10907304, 9923982, 9037314, 8237196, 7514766, 6862230, 6272712

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..406; the first 28 antidiagonals of array

Index entries for sequences related to factorial base representation

Formula

A(1,k) = A265905(k); and for n > 1, A(n,k) = A(n-1, k+1) - A(n-1, k).

Example

The top left 7 x 8 corner of the array:
      1, 3, 11, 49, 291, 1979, 15217
      2, 8, 38, 242, 1688, 13238, 121442
      6, 30, 204, 1446, 11550, 108204, 1091526
     24, 174, 1242, 10104, 96654, 983322, 10907304
    150, 1068, 8862, 86550, 886668, 9923982, 123958350
    918, 7794, 77688, 800118, 9037314, 114034368, 1514355678
   6876, 69894, 722430, 8237196, 104997054, 1400321310, 20026187676
  63018, 652536, 7514766, 96759858, 1295324256, 18625866366, 291196957578

Prog

(Scheme)
(define (A275950 n) (A275950bi (A002260 n) (A004736 n)))
(define (A275950bi row col) (if (= 1 row) (A265905 col) (- (A275950bi (- row 1) (+ 1 col)) (A275950bi (- row 1) col))))

Crossrefs

Transpose: A275951.

Row 1: A265905, row 2: A265906, row 3: A275953.

Column 1: A275955.

Cf. A153880.

Variant: A275960.

Sequence in context: A344891 A163841 A276589 * A276587 A180185 A072634

Adjacent sequences: A275947 A275948 A275949 * A275951 A275952 A275953

Keyword

nonn,tabl

Author

Antti Karttunen, Aug 13 2016

Status

approved