The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A171486

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A171486

Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A033321.
(history; published version)

#10 by N. J. A. Sloane at Sun Sep 08 19:59:25 EDT 2013

FORMULA

T(n,k) = T(n-1,k-1) + T(n-1,k) + sum_{i, i>=0} T(n-1,k+1+i)*2^i. - _Philippe Deléham, _, Feb 23 2012

Discussion

Sun Sep 08

19:59

OEIS Server: https://oeis.org/edit/global/1941

#9 by N. J. A. Sloane at Sun Sep 08 13:31:52 EDT 2013

AUTHOR

_Philippe DELEHAM_, Deléham_, Dec 09 2009

Discussion

Sun Sep 08

13:31

OEIS Server: https://oeis.org/edit/global/1938

#8 by N. J. A. Sloane at Fri Feb 22 14:39:41 EST 2013

FORMULA

T(n,k) = T(n-1,k-1) + T(n-1,k) + sum_{i, i>=0} T(n-1,k+1+i)*2^i. - DELEHAM Philippe, Deléham, Feb 23 2012

Discussion

Fri Feb 22

14:39

OEIS Server: https://oeis.org/edit/global/1863

#7 by Russ Cox at Sat Mar 31 10:28:09 EDT 2012

AUTHOR

_Philippe DELEHAM (kolotoko(AT)wanadoo.fr), _, Dec 09 2009

Discussion

Sat Mar 31

10:28

OEIS Server: https://oeis.org/edit/global/535

#6 by Bruno Berselli at Fri Feb 24 05:47:21 EST 2012

STATUS

editing

approved

#5 by Bruno Berselli at Fri Feb 24 05:47:17 EST 2012

FORMULA

T(n,k) = T(n-1,k-1) + T(n-1,k) + Sum_sum_{i, i>=0} T(n-1,k+1+i)*2^i. - DELEHAM Philippe, Feb 23 2012

STATUS

approved

editing

#4 by Bruno Berselli at Fri Feb 24 04:58:03 EST 2012

STATUS

proposed

approved

#3 by DELEHAM Philippe at Thu Feb 23 09:26:51 EST 2012

STATUS

editing

proposed

#2 by DELEHAM Philippe at Thu Feb 23 09:26:45 EST 2012

FORMULA

T(n,k) = T(n-1,k-1) + T(n-1,k) + Sum_{i, i>=0} T(n-1,k+1+i)*2^i. - DELEHAM Philippe, Feb 23 2012

EXAMPLE

Triangle begins : 1 ; 1,1 ; 2,2,1 ; 6,5,3,1 ; 21,16,9,4,1 ; 79,58,31,14,5,1 ; ...

Triangle begins :

1

1, 1

2, 2, 1

6, 5, 3, 1

21, 16, 9, 4, 1

79, 58, 31, 14, 5, 1

311, 224, 117, 52, 20, 6, 1

STATUS

approved

editing

#1 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A033321.

DATA

1, 1, 1, 2, 2, 1, 6, 5, 3, 1, 21, 16, 9, 4, 1, 79, 58, 31, 14, 5, 1, 311, 224, 117, 52, 20, 6, 1, 1265, 900, 465, 205, 80, 27, 7, 1, 5275, 3720, 1910, 840, 330, 116, 35, 8, 1, 22431, 15713, 8034, 3532, 1396, 501, 161, 44, 9, 1, 96900, 67522, 34419, 15136, 6015, 2190

OFFSET

0,4

COMMENTS

Equal to B*A065600 = A171224*B where B = A007318 ; equal to B*A039598*B^(-2).

FORMULA

Sum_{k, 0<=k<=n} T(n,k)*x^k = A117641(n), A033321(n), A007317(n+1), A002212(n+1), A026378(n+1) for x = -1, 0, 1, 2, 3 respectively.

EXAMPLE

Triangle begins : 1 ; 1,1 ; 2,2,1 ; 6,5,3,1 ; 21,16,9,4,1 ; 79,58,31,14,5,1 ; ...

CROSSREFS

Cf. A171224, A104259, A091965

KEYWORD

nonn,tabl

AUTHOR

Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 09 2009

STATUS

approved