A275960 -id:A275960 - cp's OEIS frontend

A275965 Leftmost column of array A275960.

1, 4, 18, 216, 1794, 16050, 161748, 1754886, 20252058, 257046648, 9715067802, 169069882650, 3334258948644, 65130972856014, 1314162130657122, 27756075741907992, 599859130159322082, 13631049605170919850, 318062816759187443364, 7775218520916136276470, 195524294317191054759258, 5132224614520884668600904, 139264442985628101392954898

Offset: 1

Antti Karttunen, Aug 13 2016

nonn

Inverse binomial transform of A265907 (when both are considered as offset-0 sequences).

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

Cf. A265907, A275960.

Cf. also A275955.

(definec (A275965 n) (A275960bi n 1)) ;; A275960bi given in A275960.

A275961 Transpose of array A275960.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Aug 13 2016

See A275960.

Transpose: A275960.

(define (A275961 n) (A275960bi (A004736 n) (A002260 n))) ;; A275960bi given in A275960.

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), ...

Original entry on oeis.org

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

Antti Karttunen, Aug 13 2016

			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

Transpose: A275951.
Row 1: A265905, row 2: A265906, row 3: A275953.
Column 1: A275955.
Cf. A153880.
Variant: A275960.

(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))))

A(1,k) = A265905(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

A265908 a(n) = A255411(A265907(n)); also the first differences of A265907.

Original entry on oeis.org

4, 22, 256, 2500, 24598, 262192, 3005356, 36562174, 478487968, 12927533332, 280630789030, 5778343352464, 118583043104764, 2476606038823342, 53484469903211776, 1188931280602126420, 27430026590262346558, 653821165282804596712, 16172901278558141600116, 413537682797697142621894, 10959122779052635897843288, 300659352550430117464479652

Offset: 1

Antti Karttunen, Dec 20 2015

In factorial base (A007623) these numbers are almost just like those of A265906, but shifted once left, with an extra zero appended, and then each nonzero digit incremented by one:

20, 320, 20220, 324020, 4604320, 64004220, 824203020, , ...

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

Row 2 of A275960.
Cf. A007623, A255411.
First differences of A265907.

a(n) = A255411(A265907(n))

a(n) = A265907(n+1) - A265907(n).

A275963 First differences of A265908; second differences of A265907.

Original entry on oeis.org

18, 234, 2244, 22098, 237594, 2743164, 33556818, 441925794, 12449045364, 267703255698, 5497712563434, 112804699752300, 2358022995718578, 51007863864388434, 1135446810698914644, 26241095309660220138, 626391138692542250154, 15519080113275337003404, 397364781519139001021778, 10545585096254938755221394, 289700229771377481566636364

Offset: 1

Antti Karttunen, Aug 13 2016

Antti Karttunen, Table of n, a(n) for n = 1..52
Index entries for sequences related to factorial base representation

Row 3 of A275960.

Cf. A265907, A265908.

(define (A275963 n) (- (A265908 (+ 1 n)) (A265908 n)))

a(n) = A265908(1+n) - A265908(n).

cp's OEIS Frontend

A275965 Leftmost column of array A275960.

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A275961 Transpose of array A275960.

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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), ...

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

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A265908 a(n) = A255411(A265907(n)); also the first differences of A265907.

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A275963 First differences of A265908; second differences of A265907.

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