Original entry on oeis.org
1, 2, 8, 41, 250, 1757, 13917, 122166, 1173662, 12222605, 136927351, 1639768418, 20880556880, 281460326864, 4000651782511, 59761935358025, 935445106491702, 15303039199768237, 261030618751031385, 4632889302298054713
Offset: 0
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[1] cat [(&+[Binomial(n+(n-1)*(j+1), n*(j+1)-1): j in [0..n]]): n in [1..30]]; // G. C. Greubel, Mar 09 2021
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Table[Sum[Binomial[n^2 -(n-1)*(j-1), j], {j,0,n}], {n,0,30}] (* G. C. Greubel, Mar 09 2021 *)
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[sum(binomial(n^2 -(n-1)*(j-1), j) for j in (0..n)) for n in (0..30)] # G. C. Greubel, Mar 09 2021
Original entry on oeis.org
1, 2, 4, 9, 22, 57, 155, 441, 1311, 4066, 13130, 44046, 153144, 550706, 2044248, 7819897, 30779570, 124487688, 516723174, 2198726181, 9581247648, 42717268934, 194688593966, 906331074605, 4306472500778, 20871165469241, 103106015116437
Offset: 0
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A099239:= func< n,k | (&+[Binomial(k*(n-k) -(k-1)*(j-1), j): j in [0..n-k]]) >;
[(&+[A099239(n,j): j in [0..n]]): n in [0..30]]; // G. C. Greubel, Mar 09 2021
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A099239[n_, k_]:= Sum[Binomial[k*(n-k) -(k-1)*(j-1), j], {j,0,n-k}];
Table[Sum[A099239[n, k], {k,0,n}], {n,0,30}] (* G. C. Greubel, Mar 09 2021 *)
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def A099239(n,k): return sum(binomial(k*(n-k)-(k-1)*(j-1), j) for j in (0..n-k))
[sum(A099239(n,k) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Mar 09 2021
A099253
(7*n+6)-th terms of expansion of 1/(1-x-x^7).
Original entry on oeis.org
1, 8, 43, 211, 1030, 5055, 24851, 122166, 600470, 2951330, 14505951, 71297834, 350434385, 1722411860, 8465785506, 41609980404, 204516223418, 1005212819668, 4940697593195, 24283905085013, 119357243593561, 586649945651116
Offset: 0
- G. C. Greubel, Table of n, a(n) for n = 0..500
- D. Birmajer, J. B. Gil, and M. D. Weiner, On the Enumeration of Restricted Words over a Finite Alphabet, J. Int. Seq. 19 (2016) # 16.1.3, example 16.
- Index entries for linear recurrences with constant coefficients, signature (8,-21,35,-35,21,-7,1).
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[(&+[Binomial(7*n-6*j+6,j): j in [0..n]]): n in [0..30]]; // G. C. Greubel, Mar 09 2021
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Table[Sum[Binomial[7*n-6*(j-1), j], {j,0,n}], {n,0,30}] (* G. C. Greubel, Mar 09 2021 *)
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[sum(binomial(7*n-6*j+6,j) for j in (0..n)) for n in (0..30)] # G. C. Greubel, Mar 09 2021
A099242
(6n+5)-th terms of expansion of 1/(1 - x - x^6).
Original entry on oeis.org
1, 7, 34, 153, 686, 3088, 13917, 62721, 282646, 1273690, 5739647, 25864698, 116554700, 525233175, 2366870474, 10665883415, 48063918336, 216591552484, 976031547888, 4398313653120, 19820223058176, 89316331907533
Offset: 0
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- D. Birmajer, J. B. Gil, and M. D. Weiner, On the Enumeration of Restricted Words over a Finite Alphabet, J. Int. Seq. 19 (2016) # 16.1.3, example 16.
- Index entries for linear recurrences with constant coefficients, signature (7,-15,20,-15,6,-1).
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CoefficientList[Series[1/((1 - x)^6 - x), {x, 0, 50}], x] (* G. C. Greubel, Nov 24 2017 *)
LinearRecurrence[{7,-15,20,-15,6,-1},{1,7,34,153,686,3088},30] (* Harvey P. Dale, May 06 2018 *)
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my(x='x+O('x^50)); Vec(1/((1-x)^6-x)) \\ G. C. Greubel, Nov 24 2017
Showing 1-4 of 4 results.
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