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A275328
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Triangle read by rows, Riordan array [1, (1+x/(1-4*x^2))/sqrt(1-4*x^2)].
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2
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1, 0, 1, 0, 2, 1, 0, 6, 4, 1, 0, 6, 16, 6, 1, 0, 30, 36, 30, 8, 1, 0, 20, 120, 98, 48, 10, 1, 0, 140, 232, 342, 200, 70, 12, 1, 0, 70, 756, 924, 784, 350, 96, 14, 1, 0, 630, 1300, 2856, 2576, 1550, 556, 126, 16, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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LINKS
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EXAMPLE
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Table starts:
[n] [k=0,1,2,...] row sum
[0], [1], 1
[1], [0, 1], 1
[2], [0, 2, 1], 3
[3], [0, 6, 4, 1], 11
[4], [0, 6, 16, 6, 1], 29
[5], [0, 30, 36, 30, 8, 1], 105
[6], [0, 20, 120, 98, 48, 10, 1], 297
[7], [0, 140, 232, 342, 200, 70, 12, 1], 997
[8], [0, 70, 756, 924, 784, 350, 96, 14, 1], 2995
[9], [0, 630, 1300, 2856, 2576, 1550, 556, 126, 16, 1], 9611
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MAPLE
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S := proc(n, k) option remember; local sf: if n = 0 then return n^k fi;
sf := n -> n!/iquo(n, 2)!^2; add(sf(i)*S(n-1, k-i), i=1..k-n+1) end:
A275328 := (n, k) -> S(k, n): seq(seq(A275328(n, k), k=0..n), n=0..8);
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MATHEMATICA
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(* The function RiordanArray is defined in A256893. *)
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PROG
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(SageMath) # uses[riordan_array from A256893]
riordan_array(1, (1+x/(1-4*x^2))/sqrt(1-4*x^2), 10)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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