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A108267 Triangle, read by rows, where row n has g.f.: (1-x)^(n+1)*[Sum_{j=0..n} C(n+n*j+j,n*j+j)*x^j]. 8
1, 1, 1, 1, 7, 1, 1, 31, 31, 1, 1, 121, 381, 121, 1, 1, 456, 3431, 3431, 456, 1, 1, 1709, 26769, 60691, 26769, 1709, 1, 1, 6427, 193705, 848443, 848443, 193705, 6427, 1, 1, 24301, 1343521, 10350421, 19610233, 10350421, 1343521, 24301, 1, 1, 92368 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are A000169(n) = (n+1)^n. Column 1 forms A048775(n) = binomial(2*n+1,n+1)-(n+1).

G.f. of row n divided by (1-x)^(n+1) equals g.f. of row n of table A060543. Matrix product of this triangle with Pascal's triangle (A007318) equals A108291.

LINKS

Table of n, a(n) for n=0..46.

FORMULA

Sum_{k=0..n} T(n, k)*2^k = A108292(n).

EXAMPLE

Triangle begins:

1;

1,1;

1,7,1;

1,31,31,1;

1,121,381,121,1;

1,456,3431,3431,456,1;

1,1709,26769,60691,26769,1709,1;

1,6427,193705,848443,848443,193705,6427,1; ...

G.f. of row 3: (1 + 31*x + 31*x^2 + x^3) = (1-x)^4*(1 + 35*x + 165*x^2 + 455*x^3 +... + C(4*j+3,4*j)*x^j +...).

PROG

(PARI) T(n, k)=polcoeff((1-x)^(n+1)*sum(j=0, n, binomial(n+n*j+j, n*j+j)*x^j), k)

CROSSREFS

Cf. A108267, A000169, A048775.

Cf. A060543, A108291, A108292.

Sequence in context: A248829 A154337 A033933 * A156916 A173584 A166973

Adjacent sequences:  A108264 A108265 A108266 * A108268 A108269 A108270

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, May 29 2005 and May 31 2005

STATUS

approved

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Last modified November 12 12:43 EST 2018. Contains 317109 sequences. (Running on oeis4.)