A275965 -id:A275965 - cp's OEIS frontend

A275960 Square array A(1,k) = A265907(k), A(n>1,k) = A(n-1, k+1) - A(n-1, k); successive differences of A265907 read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

1, 5, 4, 27, 22, 18, 283, 256, 234, 216, 2783, 2500, 2244, 2010, 1794, 27381, 24598, 22098, 19854, 17844, 16050, 289573, 262192, 237594, 215496, 195642, 177798, 161748, 3294929, 3005356, 2743164, 2505570, 2290074, 2094432, 1916634, 1754886, 39857103, 36562174, 33556818, 30813654, 28308084, 26018010, 23923578, 22006944, 20252058

Offset: 1

Antti Karttunen, Aug 13 2016

			The top left corner of the array:
       1, 5, 27, 283, 2783, 27381, 289573
       4, 22, 256, 2500, 24598, 262192, 3005356
      18, 234, 2244, 22098, 237594, 2743164, 33556818
     216, 2010, 19854, 215496, 2505570, 30813654, 408368976
    1794, 17844, 195642, 2290074, 28308084, 377555322, 11598750594
   16050, 177798, 2094432, 26018010, 349247238, 11221195272, 231648340170
  161748, 1916634, 23923578, 323229228, 10871948034, 220427144898, ...

Transpose: A275961.
Row 1: A265907, row 2: A265908, row 3: A275963.
Column 1: A275965.
Cf. A255411.
Variant: A275950.

(define (A275960 n) (A275960bi (A002260 n) (A004736 n)))
(define (A275960bi row col) (if (= 1 row) (A265907 col) (- (A275960bi (- row 1) (+ 1 col)) (A275960bi (- row 1) col))))

A(1,k) = A265907(k); and for n > 1, A(n,k) = A(n-1, k+1) - A(n-1, k).

A265907 a(1) = 1; for n > 1, a(n) = a(n-1) + A255411(a(n-1)).

Original entry on oeis.org

1, 5, 27, 283, 2783, 27381, 289573, 3294929, 39857103, 518345071, 13445878403, 294076667433, 6072420019897, 124655463124661, 2601261501948003, 56085731405159779, 1245017012007286199, 28675043602269632757, 682496208885074229469, 16855397487443215829585, 430393080285140358451479, 11389515859337776256294767

Offset: 1

Antti Karttunen, Dec 20 2015

In factorial base (A007623) these numbers look as:

1, 21, 1011, 21301, 350321, 5300311, 71310201, 905513221, , ...

Antti Karttunen, Table of n, a(n) for n = 1..120
Index entries for sequences related to factorial base representation

Row 1 of A275960.
Binomial transform of A275965 (when both are considered as offset-0 sequences).
Cf. A007623, A255411.
Cf. A265908 (first differences), A265905 (variant).
Subsequence of A256450.

a(1) = 1; for n > 1, a(n) = a(n-1) + A255411(a(n-1)).

Note about binomial transform corrected - Antti Karttunen, Sep 20 2016

A275955 Leftmost column of array A275950.

Original entry on oeis.org

1, 2, 6, 24, 150, 918, 6876, 63018, 589518, 6272712, 76110150, 950826294, 13044895668, 197045295354, 3070861314894, 51493780503216, 931608094164870, 17371288788509142, 344019296960858844, 7251768315234745722, 157314435990604845822, 3591397708609454572248, 86444118766100900895390

Offset: 1

Antti Karttunen, Aug 13 2016

nonn

Inverse binomial transform of A265905 (when both are considered as offset-0 sequences).

Antti Karttunen, Table of n, a(n) for n = 1..32

Cf. A265905, A275950.

Cf. also A275965.

(define (A275955 n) (A275950bi n 1)) ;; A275950bi given in A275950.

cp's OEIS Frontend

A275960 Square array A(1,k) = A265907(k), A(n>1,k) = A(n-1, k+1) - A(n-1, k); successive differences of A265907 read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

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A265907 a(1) = 1; for n > 1, a(n) = a(n-1) + A255411(a(n-1)).

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A275955 Leftmost column of array A275950.

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