The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A247237 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A247237

Triangle read by rows: T(n,k) is the coefficient in the transformation Sum_{k=0..n} (k+1)*x^k = Sum_{k=0..n} T(n,k)*(x-k)^k.
(history; published version)

#18 by Joerg Arndt at Tue Apr 26 12:31:53 EDT 2016

STATUS

proposed

approved

#17 by Michel Marcus at Tue Apr 26 11:57:51 EDT 2016

STATUS

editing

proposed

#16 by Michel Marcus at Tue Apr 26 11:57:45 EDT 2016

EXTENSIONS

Edited. _ by _Wolfdieter Lang_, Jan 14 2015

STATUS

proposed

editing

#15 by Andrew Howroyd at Tue Apr 26 11:56:20 EDT 2016

STATUS

editing

proposed

#14 by Andrew Howroyd at Tue Apr 26 11:56:16 EDT 2016

KEYWORD

nonn,tabl

STATUS

approved

editing

#13 by Wolfdieter Lang at Wed Jan 14 15:26:43 EST 2015

STATUS

editing

approved

#12 by Wolfdieter Lang at Wed Jan 14 15:26:38 EST 2015

EXTENSIONS

EditredEdited. Wolfdieter Lang, Jan 14 2015

STATUS

approved

editing

#11 by Wolfdieter Lang at Wed Jan 14 15:26:15 EST 2015

STATUS

editing

approved

#10 by Wolfdieter Lang at Wed Jan 14 15:26:08 EST 2015

EXTENSIONS

Editred. Wolfdieter Lang, Jan 14 2015

#9 by Wolfdieter Lang at Wed Jan 14 15:25:47 EST 2015

NAME

Triangle read by rows: T(n,k) is the coefficient A_k in the transformation Sum_{k=0..n} (k+1)*x^k = Sum_{k=0..n} A_T(n,k)*(x-k)^k.

COMMENTS

Consider the transformation 1 + 2x + 3x^2 + 4x^3 + ... + (n+1)*x^n = A_T(n,0)*(x-0)^0 + A_T(n,1)*(x-1)^1 + A_T(n,2)*(x-2)^2 + ... + A_T(n,n)*(x-n)^n. This sequence gives A_0, ... A_n as the entries in the n-th row of this triangle, starting at , for n >= 0.

FORMULA

T(n,n) = n+1, n >= 0.

EXAMPLE

From Wolfdieter Lang, Jan 14 2015: (Start)

Triangle The triangle T(n,k) starts:

n\k 0 1; 2 3 4 5 6 7 8 9 ...

0: 1

1: 3, 2;

2: 3, 14, 3;

3, : 3 50, 39, 4;

4: 3, 130, 279, 84, 5;

5: 3, 280, 1479, 984, 155, 6;

6: 3, 532, 6519, 8544, 2675, 258, 7;

7: 3, 924, 25335, 61464, 34035, 6138, 399, 8;

8: 3, 1500, 89847, 388056, 356595, 106938, 12495, 584, 9;

9: 3, 2310, 297207, 2225136, 3259635, 1524438, 284655, 23264, 819, 10;

...

-----------------------------------------------------------------

n = 3: 1 + 2*x + 3*x^2 + 4*x^3 = 3*(x-0)^0 + 50*(x-1)^1 + 39*(x-2)^2 + 4*(x-3)^3.

(End)

CROSSREFS

Cf. A247236, A153978, A027444, A253381.

STATUS

approved

editing