A112463 -id:A112463 - cp's OEIS frontend

A112461 Absolute value of coefficient of term [x^(n-5)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 5. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.

5, 59, 374, 1694, 6149, 19019, 52052, 129272, 296582, 636922, 1293292, 2502604, 4644094, 8306914, 14382544, 24188824, 39633715, 63428365, 99360690, 152642490, 230345115, 341940885, 499969860, 720854160, 1025884860, 1442409540, 2005251864, 2758398104

Offset: 5

Paul Max Payton, Sep 23 2005

T. D. Noe and Bruno Berselli, Table of n, a(n) for n = 5..1004
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Cf. A000217, A000914, A001844, A112459, A112460, A112462, A112463, A112464.

Table[(9n+5)/10! Product[n+i,{i,-4,4}],{n,5,40}] (* Harvey P. Dale, Apr 26 2019 *)

a(n) = ((9n+5)/10!) * Product_{i=-4..4} (n+i).

G.f.: x^5*(5+4*x)/(1-x)^11. - Colin Barker, Mar 28 2012

Offset changed from 1 to 5, formulas and b-file adapted by Bruno Berselli, Mar 29 2012

A112462 Absolute value of coefficient of term [x^(n-6)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 6. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.

Original entry on oeis.org

6, 83, 611, 3185, 13195, 46228, 142324, 395148, 1007760, 2393430, 5349526, 11345698, 22985326, 44722580, 83947700, 152591660, 269449830, 463484385, 778439025, 1279189275, 2060359665, 3257868120, 5064210840, 7748481000, 11682325200, 17373286476, 25507265868

Offset: 6

Paul Max Payton, Sep 23 2005

T. D. Noe and Bruno Berselli, Table of n, a(n) for n = 6..1005

Cf. A000217, A000914, A001844, A112459, A112460, A112461, A112463, A112464.

a(n) = ((11n+6)/12!) * Product_{i=-5..5} (n+i).

G.f.: x^6*(6+5*x)/(1-x)^13. - Colin Barker, Mar 28 2012

Offset changed from 1 to 6, formulas and b-file adapted by Bruno Berselli, Mar 29 2012

A112464 Absolute value of coefficient of term [x^(n-8)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 8. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.

Original entry on oeis.org

8, 143, 1343, 8823, 45543, 196707, 739347, 2483547, 7599867, 21492097, 56794705, 141485305, 334639305, 755863605, 1638428805, 3422280285, 6912424485, 13541987610, 25799313210, 47907161610, 86882479530, 154161302130, 268050218130, 457369908930, 766795640130

Offset: 8

Paul Max Payton, Sep 23 2005

Vincenzo Librandi and Bruno Berselli, Table of n, a(n) for n = 8..10008

Cf. A000217, A000914, A001844, A112459, A112460, A112461, A112462, A112463.

Table[(Times@@(n+Range[0,14])(15n+113))/16!,{n,30}] (* or *) CoefficientList[ Series[ (-8-7 x)/(-1+x)^17,{x,0,30}],x] (* Harvey P. Dale, Jul 24 2011 *)

a(n) = ((15n+8)/16!) * Product_{i=-7..7} (n+i).

G.f.: x^8*(8+7*x)/(1-x)^17. - Harvey P. Dale, Jul 24 2011

More terms from Harvey P. Dale, Jul 24 2011

Offset changed from 0 to 8, formulas and b-file adapted by Bruno Berselli, Mar 29 2012

A112459 Absolute value of coefficient of term [x^(n-3)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 3. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.

Original entry on oeis.org

3, 23, 98, 308, 798, 1806, 3696, 6996, 12441, 21021, 34034, 53144, 80444, 118524, 170544, 240312, 332367, 452067

Offset: 3

Paul Max Payton, Sep 23 2005

Cf. A000217, A000914, A001844, A112460, A112461, A112462, A112463, A112464.

a(n) = n*(n^2-4)*(n^2-1)*(5*n+3)/6!.

G.f.: x^3*(3+2*x)/(1-x)^7. - Colin Barker, Mar 28 2012

Offset changed from 1 to 3 and formulas adapted by Bruno Berselli, Mar 29 2012

A112460 Absolute value of coefficient of term [x^(n-4)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 4. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.

Original entry on oeis.org

4, 39, 207, 795, 2475, 6633, 15873, 34749, 70785, 135850, 247962, 433602, 730626, 1191870, 1889550, 2920566, 4412826, 6532713, 9493825, 13567125, 19092645, 26492895, 36288135, 49113675, 65739375, 87091524, 114277284, 148611892, 191648820, 245213100, 311438028

Offset: 4

Paul Max Payton, Sep 23 2005

Cf. A000217, A000914, A001844, A112459, A112461, A112462, A112463, A112464.

Drop[Table[(7n^8+4n^7-98n^6-56n^5+343n^4+196n^3-252n^2-144n)/40320,{n,40}],3] (* Harvey P. Dale, Dec 15 2013 *)

a(n) = (n-3)*(n-2)*(n-1)*n*(n+1)*(n+2)*(n+3)*(7*n+4)/8!.

G.f.: x^4*(4+3*x)/(1-x)^9. - Colin Barker, Mar 28 2012

cp's OEIS Frontend

A112461 Absolute value of coefficient of term [x^(n-5)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 5. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.

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A112462 Absolute value of coefficient of term [x^(n-6)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 6. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.

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A112464 Absolute value of coefficient of term [x^(n-8)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 8. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.

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A112459 Absolute value of coefficient of term [x^(n-3)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 3. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.

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A112460 Absolute value of coefficient of term [x^(n-4)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 4. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.

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