Original entry on oeis.org
1, 7, 31, 101, 272, 636, 1340, 2600, 4725, 8135, 13391, 21217, 32536, 48496, 70512, 100296, 139905, 191775, 258775, 344245, 452056, 586652, 753116, 957216, 1205477, 1505231, 1864695, 2293025, 2800400, 3398080, 4098496, 4915312
Offset: 3
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CoefficientList[Series[(1+2*x+4*x^2+2*x^3+x^4)/((1-x)^7*(1+x)^2), {x, 0, 40}], x] (* Georg Fischer, Aug 16 2021 *)
A247644
Triangle formed from the odd-numbered rows of A088855.
Original entry on oeis.org
1, 1, 1, 1, 1, 2, 4, 2, 1, 1, 3, 9, 9, 9, 3, 1, 1, 4, 16, 24, 36, 24, 16, 4, 1, 1, 5, 25, 50, 100, 100, 100, 50, 25, 5, 1, 1, 6, 36, 90, 225, 300, 400, 300, 225, 90, 36, 6, 1, 1, 7, 49, 147, 441, 735, 1225, 1225, 1225, 735, 441, 147, 49, 7, 1, 1, 8, 64, 224, 784, 1568, 3136, 3920, 4900, 3920, 3136, 1568, 784, 224, 64, 8, 1
Offset: 1
Triangle begins:
1,
1,1,1,
1,2,4,2,1,
1,3,9,9,9,3,1,
1,4,16,24,36,24,16,4,1,
1,5,25,50,100,100,100,50,25,5,1,
1,6,36,90,225,300,400,300,225,90,36,6,1,
1,7,49,147,441,735,1225,1225,1225,735,441,147,49,7,1,
1,8,64,224,784,1568,3136,3920,4900,3920,3136,1568,784,224,64,8,1,
...
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row[n_] := CoefficientList[Sum[Binomial[n, k]^2 *x^(2*k), {k, 0, n}] + Sum[Binomial[n, k]*Binomial[n, k - 1]* x^(2*k - 1), {k, 0, n}], x];
Table[row[n], {n, 0, 8}] // Flatten (* Jean-François Alcover, Jun 07 2018 *)
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T(n, k) = binomial((n-1)\2, (k-1)\2)*binomial(n\2, k\2); \\ A088855
row(n) = vector(2*n-1, k, T(2*n-1, k)); \\ Michel Marcus, Sep 27 2021
Showing 1-2 of 2 results.
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