A265905 -id:A265905 - cp's OEIS frontend

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

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).

A265906 a(n) = A153880(A265905(n)); also the first differences of A265905.

Original entry on oeis.org

2, 8, 38, 242, 1688, 13238, 121442, 1212968, 13211798, 160076282, 2080120448, 28952201678, 436718865962, 6985509376688, 118290516617198, 2137197890239202, 40600129761103688, 809755594446845558, 17050115848925513762, 375062123907891088808, 8608573107134508912038, 207014026157802769184402, 5174962975935097945559048

Offset: 1

Antti Karttunen, Dec 20 2015

In factorial base (A007623) these numbers are just like those in A265905, but shifted once left, with an extra zero appended:

10, 110, 1210, 20010, 220110, 2421210, 30040010, 330440110, 3635241210, 40111110010, 441222210110, 4853444311210, 50188010430010, , ...

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

Row 2 of A275950.
First differences of A265905.
Cf. A007623, A153880.

a(n) = A153880(A265905(n)).

a(n) = A265905(n+1) - A265905(n).

A275953 First differences of A265906; second differences of A265905.

Original entry on oeis.org

6, 30, 204, 1446, 11550, 108204, 1091526, 11998830, 146864484, 1920044166, 26872081230, 407766664284, 6548790510726, 111305007240510, 2018907373622004, 38462931870864486, 769155464685741870, 16240360254478668204, 358012008058965575046, 8233510983226617823230, 198405453050668260272364, 4967948949777295176374646, 129158062469199137001844830

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 A275950.

Cf. A265905, A265906.

(define (A275953 n) (- (A265906 (+ 1 n)) (A265906 n)))

a(n) = A265906(1+n) - A265906(n).

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

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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A265906 a(n) = A153880(A265905(n)); also the first differences of A265905.

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A275953 First differences of A265906; second differences of A265905.

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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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