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Revision History for A112008

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A112008

Fourth diagonal of second-order Eulerian triangle A008517. Fourth column (m=3) of triangle A112007.
(history; published version)

#7 by R. J. Mathar at Tue Oct 09 04:35:08 EDT 2012

STATUS

editing

approved

#6 by R. J. Mathar at Tue Oct 09 04:35:02 EDT 2012

AUTHOR

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Sep 12 2005

Wolfdieter Lang, Sep 12 2005

STATUS

approved

editing

#5 by Russ Cox at Fri Mar 30 18:59:44 EDT 2012

FORMULA

Contribution from _Johannes W. Meijer (meijgia(AT)hotmail.com), _, Oct 16 2009: (Start)

CROSSREFS

Contribution from _Johannes W. Meijer (meijgia(AT)hotmail.com), _, Oct 16 2009: (Start)

Discussion

Fri Mar 30

18:59

OEIS Server: https://oeis.org/edit/global/295

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

FORMULA

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009: (Start)

a(n) = sum((-1)^(n+k)*binomial(2*n+9,k)*stirling1(n-k+8,4-k), k=0..3)

(End)

CROSSREFS

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009: (Start)

Equals fourth left hand column of A163936.

(End)

KEYWORD

nonn,easy,new

#3 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

FORMULA

a(n)=A112007(n+3, 3), n>=0.

KEYWORD

nonn,easy,new

#2 by N. J. A. Sloane at Tue Jan 24 03:00:00 EST 2006

CROSSREFS

Cf. A002539 (3rd diagonal of A008517 ; third column of A112007).

KEYWORD

nonn,easy,new

#1 by N. J. A. Sloane at Wed Sep 21 03:00:00 EDT 2005

NAME

Fourth diagonal of second-order Eulerian triangle A008517. Fourth column (m=3) of triangle A112007.

DATA

1, 52, 1452, 32120, 644020, 12440064, 238904904, 4642163952, 92199790224, 1883079661824, 39689578055808, 865023253219584, 19515249341231616, 455924361142656000, 11030149104146035200, 276260563641659673600

OFFSET

0,2

FORMULA

a(n)=A112007(n+3,3), n>=0.

a(n)= (n+7)*a(n-1) + (n+1)*A002539(n+1), n>=1, a(0)=1.

EXAMPLE

1452= a(2) = 9*52 + 3*328.

CROSSREFS

Cf. A002539 (3rd diagonal of A008517 ; third column of A112007).

KEYWORD

nonn,easy,new

AUTHOR

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Sep 12 2005

STATUS

approved