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A137156 Matrix inverse of triangle A137153(n,k) = C(2^k+n-k-1, n-k), read by rows. 6
1, -1, 1, 1, -2, 1, -2, 5, -4, 1, 9, -24, 22, -8, 1, -88, 239, -228, 92, -16, 1, 1802, -4920, 4749, -1976, 376, -32, 1, -75598, 206727, -200240, 84086, -16432, 1520, -64, 1, 6421599, -17568408, 17034964, -7173240, 1413084, -133984, 6112, -128, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Unsigned column 0 = A001192, number of full sets of size n.

LINKS

Table of n, a(n) for n=0..44.

FORMULA

G.f. of column k: 1 = Sum_{n>=0} T(n+k,k)*x^n/(1-x)^(2^(n+k)).

EXAMPLE

Triangle begins:

1;

-1, 1;

1, -2, 1;

-2, 5, -4, 1;

9, -24, 22, -8, 1;

-88, 239, -228, 92, -16, 1;

1802, -4920, 4749, -1976, 376, -32, 1;

-75598, 206727, -200240, 84086, -16432, 1520, -64, 1;

6421599, -17568408, 17034964, -7173240, 1413084, -133984, 6112, -128, 1; ...

PROG

(PARI) /* As matrix inverse of A137153: */

{T(n, k) = local(M=matrix(n+1, n+1, r, c, if(r>=c, binomial(2^(c-1)+r-c-1, r-c)))); if(n<k||k<0, 0, (M^-1)[n+1, k+1])}

for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))

(PARI) /* Using the g.f.: */

{T(n, k) = if(n<k||k<0, 0, if(n==k, 1, polcoeff(1-sum(j=0, n-k-1, T(j+k, k)*x^j/(1-x+x*O(x^(n-k)))^(2^(j+k))), n-k)))}

for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))

CROSSREFS

Cf. A137153 (matrix inverse); unsigned columns: A001192, A137157, A137158, A137159; unsigned row sums: A137160.

Sequence in context: A337991 A104560 A121435 * A136457 A209133 A078016

Adjacent sequences:  A137153 A137154 A137155 * A137157 A137158 A137159

KEYWORD

sign,tabl

AUTHOR

Paul D. Hanna, Jan 24 2008

STATUS

approved

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Last modified January 25 21:23 EST 2021. Contains 340427 sequences. (Running on oeis4.)