A183066
G.f.: A(x) = (1 + 21*x + 3*x^2 - x^3)/(1-x)^5.
Original entry on oeis.org
1, 26, 123, 364, 845, 1686, 3031, 5048, 7929, 11890, 17171, 24036, 32773, 43694, 57135, 73456, 93041, 116298, 143659, 175580, 212541, 255046, 303623, 358824, 421225, 491426, 570051, 657748, 755189, 863070, 982111, 1113056, 1256673, 1413754, 1585115, 1771596
Offset: 0
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.
Original entry on oeis.org
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
Offset: 0
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; ...
-
{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)}
A183067
G.f.: A(x) = Sum_{n>=0} (4n)!/n!^4 * x^(2n)/(1-2*x)^(4n+1).
Original entry on oeis.org
1, 2, 28, 248, 3976, 52112, 850144, 13032896, 217878616, 3594283952, 61577419168, 1056910842176, 18485891235904, 325146542386304, 5781811796793088, 103413141115923968, 1863085674077321176, 33737014083314312624
Offset: 0
Showing 1-3 of 3 results.
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