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Revision History for A113148

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Row 7 of table A113143; equal to INVERT of 7-fold factorials shifted one place right.
(history; published version)
#9 by N. J. A. Sloane at Sun Sep 08 13:30:50 EDT 2013
AUTHOR

_Philippe DELEHAM_ Deléham_ and Paul D. Hanna, Oct 28 2005

Discussion
Sun Sep 08
13:30
OEIS Server: https://oeis.org/edit/global/1938
#8 by Russ Cox at Sat Mar 31 10:27:53 EDT 2012
AUTHOR

_Philippe DELEHAM (kolotoko(AT)wanadoo.fr) _ and Paul D. Hanna, Oct 28 2005

Discussion
Sat Mar 31
10:27
OEIS Server: https://oeis.org/edit/global/535
#7 by Russ Cox at Fri Mar 30 18:36:51 EDT 2012
AUTHOR

Philippe DELEHAM (kolotoko(AT)wanadoo.fr) and _Paul D. Hanna (pauldhanna(AT)juno.com), _, Oct 28 2005

Discussion
Fri Mar 30
18:36
OEIS Server: https://oeis.org/edit/global/213
#6 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009
FORMULA

a(0) = 1; a(n+1) = Sum_{k=0..n} a(k)*A113136A045754(n-k).

EXAMPLE

= 1/(1 - x - x^2 - 8*x^3 - 120*x^4 -...- A113136A045754(n)*x^(n+1)

CROSSREFS

Cf. A113143, A113136 A045754 (7-fold factorials).

KEYWORD

nonn,new

nonn

#5 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007
KEYWORD

nonn,new

nonn

AUTHOR

Philippe DELEHAM (kolotoko(AT)wanadoo.fr) and Paul D . Hanna (pauldhanna(AT)juno.com), Oct 28 2005

#4 by N. J. A. Sloane at Fri May 11 03:00:00 EDT 2007
FORMULA

a(0) = 1; a(n+1) = Sum_{k=0..n} a(k)*A113136(n-k) .

KEYWORD

nonn,new

nonn

#3 by N. J. A. Sloane at Fri May 19 03:00:00 EDT 2006
KEYWORD

nonn,new

nonn

AUTHOR

Philippe DELEHAM (kolotoko(AT)lagoonwanadoo.ncfr) and Paul D Hanna (pauldhanna(AT)juno.com), Oct 28 2005

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

a(n) = Sum_{j=0..k} 7^(k-j)*A111146(k, j).

KEYWORD

nonn,new

nonn

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

Row 7 of table A113143; equal to INVERT of 7-fold factorials shifted one place right.

DATA

1, 1, 2, 11, 141, 2928, 82597, 2925973, 124502114, 6179425823, 350316271761, 22326710345256, 1579953165170881, 122905129550802985, 10423661531476766834, 957176457621821573987, 94608465923392572536421

OFFSET

0,3

FORMULA

a(n) = Sum_{j=0..k} 7^(k-j)*A111146(k,j).

a(0) = 1; a(n+1) = Sum_{k=0..n} a(k)*A113136(n-k) .

EXAMPLE

A(x) = 1 + x + 2*x^2 + 11*x^3 + 141*x^4 + 2928*x^5 +...

= 1/(1 - x - x^2 - 8*x^3 - 120*x^4 -...- A113136(n)*x^(n+1)

-...).

PROG

(PARI) {a(n)=local(x=X+X*O(X^n)); A=1/(1-x-x^2*sum(j=0, n, x^j*prod(i=0, j, 7*i+1))); return(polcoeff(A, n, X))}

CROSSREFS

Cf. A113143, A113136 (7-fold factorials).

KEYWORD

nonn

AUTHOR

Philippe DELEHAM (kolotoko(AT)lagoon.nc) and Paul D Hanna (pauldhanna(AT)juno.com), Oct 28 2005

STATUS

approved