A175699 -id:A175699 - cp's OEIS frontend

A202717 Triangle of numerators of coefficients of the polynomial Q^(3)m(n) defined by the recursion Q^(3)_0(n)=1; for m>=1, Q^(3)_m(n) = Sum{i=1...n} i^3*Q^(3)_(m-1)(i).

1, 1, 2, 1, 0, 0, 21, 132, 294, 252, 21, -56, 0, 8, 0, 35, 450, 2293, 5700, 6405, 770, -3661, -240, 2320, 40, -672, 0, 0, 9555, 207480, 1889316, 9216312, 25051026, 33229560, 3678948, -35339304, -2666157, 51171120, 2178176, -49878192, -792064, 24460800, 4160, -3714816, 0

Offset: 0

Vladimir Shevelev and Peter J. C. Moses, Dec 23 2011

For m>=0, the denominator for all 4*m+1 terms of the m-th row is A202368(m+1).

See comment to A175669.

			The sequence of polynomials begins
Q^(3)_0=1,
Q^(3)_1=(x^4+2*x^3+x^2)/4,
Q^(3)_2=(21*x^8+132*x^7+294*x^6+252*x^5+21*x^4-56*x^3+8*x)/672,
Q^(3)_3=(35*x^12+450*x^11+2293*x^10+5700*x^9+6405*x^8+770*x^7-3661*x^6-240*x^5+2320*x^4+40x^3-672*x^2)/13440.

Cf. A202339, A053657, A202367, A202368, A202369, A175699.

Q^(3)_n(1)=1.

A202749 Triangle of numerators of coefficients of the polynomial Q^(4)m(n) defined by the recursion Q^(4)_0(n)=1; for m>=1,Q^(4)_m(n)=sum{i=1,...,n}i^4Q^(4)(m-1)(i). For m>=0, the denominator for all 5m+1 terms of the m-th row is A202369(m+1).

Original entry on oeis.org

1, 6, 15, 10, 0, -1, 0, 36, 280, 795, 900, 88, -450, -20, 200, 1, -30, 0, 19656, 311220, 1991430, 6354075, 9367722, 1283100, -10854935, -1064700, 16237338, 615615, -16336320, -136500, 8189909, 8190, -1243800, 0

Offset: 0

Vladimir Shevelev and Peter J. C. Moses, Dec 23 2011

See comment in A175669.

			The sequence of polynomials begins
Q^(3)_0=1,
Q^(3)_1=(6*x^5+15*x^4+10*x^3-x)/30,
Q^(3)_2=(36*x^10+280*x^9+795*x^8+900*x^7+88*x^6-450*x^5-20*x^4+200*x^3+x^2-30*x)/1800.

Cf. A202339, A053657, A202367, A202368, A202369, A175699, A202717

Q^(4)_n(1)=1.

cp's OEIS Frontend

A202717 Triangle of numerators of coefficients of the polynomial Q^(3)m(n) defined by the recursion Q^(3)_0(n)=1; for m>=1, Q^(3)_m(n) = Sum{i=1...n} i^3*Q^(3)_(m-1)(i).

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A202749 Triangle of numerators of coefficients of the polynomial Q^(4)m(n) defined by the recursion Q^(4)_0(n)=1; for m>=1,Q^(4)_m(n)=sum{i=1,...,n}i^4Q^(4)(m-1)(i). For m>=0, the denominator for all 5m+1 terms of the m-th row is A202369(m+1).

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Formula

cp's OEIS Frontend

A202717 Triangle of numerators of coefficients of the polynomial Q^(3)m(n) defined by the recursion Q^(3)_0(n)=1; for m>=1, Q^(3)_m(n) = Sum{i=1...n} i^3*Q^(3)_(m-1)(i).

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Formula

A202749 Triangle of numerators of coefficients of the polynomial Q^(4)m(n) defined by the recursion Q^(4)_0(n)=1; for m>=1,Q^(4)_m(n)=sum{i=1,...,n}i^4*Q^(4)(m-1)(i). For m>=0, the denominator for all 5*m+1 terms of the m-th row is A202369(m+1).

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Author

Keywords

Comments

Examples

Crossrefs

Formula

A202749 Triangle of numerators of coefficients of the polynomial Q^(4)m(n) defined by the recursion Q^(4)_0(n)=1; for m>=1,Q^(4)_m(n)=sum{i=1,...,n}i^4Q^(4)(m-1)(i). For m>=0, the denominator for all 5m+1 terms of the m-th row is A202369(m+1).