The On-Line Encyclopedia of Integer Sequences (OEIS)

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A117270

Matrix log of triangle M = A117269, which satisfies: M - (M-I)^2 = C where C is Pascal's triangle.
(history; published version)

#4 by Russ Cox at Fri Mar 30 18:36:56 EDT 2012

AUTHOR

_Paul D. Hanna (pauldhanna(AT)juno.com), _, Mar 05 2006

Discussion

Fri Mar 30

18:36

OEIS Server: https://oeis.org/edit/global/213

#3 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

COMMENTS

E.g.f. of column 0 (A117271) is log( (3-sqrt(5-4*exp(x)))/2 ), and equals the log of the g.f. of column 0 of A117269.

KEYWORD

nonn,tabl,new

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

KEYWORD

nonn,tabl,new

AUTHOR

Paul D . Hanna (pauldhanna(AT)juno.com), Mar 05 2006

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

NAME

Matrix log of triangle M = A117269, which satisfies: M - (M-I)^2 = C where C is Pascal's triangle.

DATA

0, 1, 0, 2, 2, 0, 12, 6, 3, 0, 134, 48, 12, 4, 0, 2100, 670, 120, 20, 5, 0, 42302, 12600, 2010, 240, 30, 6, 0, 1041852, 296114, 44100, 4690, 420, 42, 7, 0, 30331814, 8334816, 1184456, 117600, 9380, 672, 56, 8, 0, 1019056260, 272986326, 37506672, 3553368

OFFSET

0,4

COMMENTS

E.g.f. of column 0 (A117271) is log( (3-sqrt(5-4*exp(x)))/2 ), and equals the log of the g.f. of column 0 of A117269.

FORMULA

T(n,k) = A117271(n-k)*C(n,k).

EXAMPLE

Triangle begins:

0;

1,0;

2,2,0;

12,6,3,0;

134,48,12,4,0;

2100,670,120,20,5,0;

42302,12600,2010,240,30,6,0;

1041852,296114,44100,4690,420,42,7,0; ...

PROG

(PARI) {a(n)=local(C=matrix(n+1, n+1, r, c, if(r>=c, binomial(r-1, c-1))), M=C, L); for(i=1, n+1, M=(M-M^0)^2+C); L=sum(r=1, #M, -(M^0-M)^r/r); return(L[n+1, 1])}

CROSSREFS

Cf. A117269, A117271 (column 0).

KEYWORD

nonn,tabl

AUTHOR

Paul D Hanna (pauldhanna(AT)juno.com), Mar 05 2006

STATUS

approved