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A183065 Triangle defined by g.f.: Sum_{n>=0} (4*n)!/n!^4 * x^(2*n)*y^n/(1-x-x*y)^(4*n+1), read by rows. 3
1, 1, 1, 1, 26, 1, 1, 123, 123, 1, 1, 364, 3246, 364, 1, 1, 845, 25210, 25210, 845, 1, 1, 1686, 120135, 606500, 120135, 1686, 1, 1, 3031, 430941, 6082475, 6082475, 430941, 3031, 1, 1, 5048, 1277668, 38698856, 137915470, 38698856, 1277668, 5048, 1, 1, 7929 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Compare the g.f. of this triangle with the g.f.s of triangles:

* A008459: Sum_{n>=0} (2n)!/n!^2 * x^(2n)*y^n/(1-x-xy)^(2n+1),

* A181543: Sum_{n>=0} (3n)!/n!^3 * x^(2n)*y^n/(1-x-xy)^(3n+1),

which have terms A008459(n,k) = C(n,k)^2 and A181543(n,k) = C(n,k)^3.

LINKS

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

EXAMPLE

G.f.: A(x,y) = 1/(1-x-xy) + 4!*x^2*y/(1-x-xy)^5 + (8!/2!^4)*x^4*y^2/(1-x-xy)^9 + (12!/3!^4)*x^6*y^3/(1-x-xy)^13 +...

Triangle begins:

1;

1, 1;

1, 26, 1;

1, 123, 123, 1;

1, 364, 3246, 364, 1;

1, 845, 25210, 25210, 845, 1;

1, 1686, 120135, 606500, 120135, 1686, 1;

1, 3031, 430941, 6082475, 6082475, 430941, 3031, 1;

1, 5048, 1277668, 38698856, 137915470, 38698856, 1277668, 5048, 1; ...

PROG

(PARI) {T(n, k)=polcoeff(polcoeff(sum(m=0, n, (4*m)!/m!^4*x^(2*m)*y^m/(1-x-x*y+x*O(x^n))^(4*m+1)), n, x), k, y)}

CROSSREFS

Cf. A183066 (column 1), A183067 (row sums), A183068 (central terms).

Sequence in context: A225532 A177970 A225483 * A157630 A173583 A040687

Adjacent sequences:  A183062 A183063 A183064 * A183066 A183067 A183068

KEYWORD

tabl,sign

AUTHOR

Paul D. Hanna, Dec 22 2010

STATUS

approved

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Last modified February 25 22:55 EST 2020. Contains 332270 sequences. (Running on oeis4.)