A144631
Second diagonal (or column) of A144630.
Original entry on oeis.org
4, 12, 880, 46900, 1615824, 45094896, 1115345088, 25519125060, 553014576400, 11514200107696, 232490008680384, 4581732884262352, 88532684825838400, 1683073282734360000, 31561148509363526400, 584964180982546208100
Offset: 2
Daniel McLaury and Ben Golub, Jan 20 2009
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[ [ &+[I[i][j]: i, j in [k..n] ]: k in [n..1 by -1] ][2] where I:=H^-1 where H:=Matrix(Rationals(), n, n, [ < i, j, 1/(i+j-1) >: i, j in [1..n] ] ): n in [2..17] ]; // Klaus Brockhaus, Jan 22 2009
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invH := proc(n,i,j) (-1)^(i+j)*(i+j-1)*binomial(n+i-1,n-j)*binomial(n+j-1,n-i)* (binomial(i+j-2,i-1))^2 ; end: A144630 := proc(n,k) local T,i,j ; T := 0 ; for i from n-k+1 to n do for j from n-k+1 to n do T := T+invH(n,i,j) ; od; od; RETURN(T) ; end: A144631 := proc(n) A144630(n+1,2) ; end: for n from 1 to 20 do printf("%a,",A144631(n)) : od: # R. J. Mathar, Jan 21 2009
Original entry on oeis.org
1, 16, 201, 3736, 95545, 2738856, 82152385, 2526574240, 78991868961, 2498812448320, 79748142780361, 2562704059745688, 82808387862053113, 2687915950092986536, 87578455481326007745, 2862650767821013111936
Offset: 1
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[ &+[ &+[I[i][j]: i, j in [k..n] ]: k in [n..1 by -1] ] where I:=H^-1 where H:=Matrix(Rationals(), n, n, [ < i, j, 1/(i+j-1) >: i, j in [1..n] ] ): n in [1..16] ]; // Klaus Brockhaus, Jan 21 2009
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invH := proc(n,i,j) (-1)^(i+j)*(i+j-1)*binomial(n+i-1,n-j)*binomial(n+j-1,n-i)* (binomial(i+j-2,i-1))^2 ; end: A144630 := proc(n,k) local T,i,j ; T := 0 ; for i from n-k+1 to n do for j from n-k+1 to n do T := T+invH(n,i,j) ; od; od; RETURN(T) ; end: A144632 := proc(n) local k; add(A144630(n,k),k=1..n) ; end: for n from 1 to 30 do printf("%a,",A144632(n)) : od: # R. J. Mathar, Jan 21 2009
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a = DifferenceRoot[Function[{y, n}, {-13632 n^5 - 136320 n^4 - 540336 n^3 - 1060896 n^2 + (-1728 n^5 - 16484 n^4 - 60648 n^3 - 106194 n^2 - 86888 n - 25970) y[n+1] + (3360 n^5 + 33600 n^4 + 154334 n^3 + 388404 n^2 + 503246 n + 257468) y[n+2] + (-1728 n^5 - 18076 n^4 - 73384 n^3 - 145038 n^2 - 140376 n - 53518) y[n+3] + (n+1)^2 (n+2)(2n + 5)(24 n + 61) y[n] + (n + 2)(n + 3)^2 (2n + 3)(24n + 35) y[n+4] - 1031616 n - 397440 == 0, y[1] == 1, y[2] == 16, y[3] == 201, y[4] == 3736}]];
Array[a, 30] (* Jean-François Alcover, Mar 31 2020 *)
Showing 1-2 of 2 results.