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
Original entry on oeis.org
1, 26, 3246, 606500, 137915470, 35218238076, 9702014515116, 2818627826459016, 851612982884556750, 265166341958122567820, 84556145346599067308596, 27489903606068331188121816, 9081510922185418532993154796
Offset: 0
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seq(simplify(binomial(2*n, n)*hypergeom([-n, -n, n+1, n+1/2], [1, 1, 1], 4)), n = 0..20);
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{a(n)=polcoeff(polcoeff(sum(m=0,2*n,(4*m)!/m!^4*x^(2*m)*y^m/(1-x-x*y+x*O(x^(2*n)))^(4*m+1)),2*n,x),n,y)}
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; ...
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{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)}
Showing 1-3 of 3 results.
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