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Search: id:A138767
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| A138767 |
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Triangle read by rows: T(n,k)=binom(n,k)*binom(2*n-2*k,n-1), n>=1, 0<=k<=floor(n/2+1/2). |
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+0
1
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| 1, 1, 4, 4, 15, 18, 3, 56, 80, 24, 210, 350, 150, 10, 792, 1512, 840, 120, 3003, 6468, 4410, 980, 35, 11440, 27456, 22176, 6720, 560, 43758, 115830, 108108, 41580, 5670, 126, 167960, 486200, 514800, 240240, 46200, 2520
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Row n contains floor(n/2+3/2) terms.
Row sums with alternate signs are 0.
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REFERENCES
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D. Beckwith, Problem 11212/11220, Amer. Math. Monthly 115, (2008), p. 366.
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EXAMPLE
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Triangle starts:
1,1;
4,4;
15,18,3;
56,18,3;
210,350,150,10;
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MAPLE
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T:=proc(n, r) options operator, arrow: binomial(n, r)*binomial(2*n-2*r, n-1) end proc: for n to 10 do seq(T(n, k), k=0..floor((1/2)*n+1/2)) end do; # yields sequence in triangular form
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CROSSREFS
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Sequence in context: A059443 A097335 A117187 this_sequence A048282 A068592 A135944
Adjacent sequences: A138764 A138765 A138766 this_sequence A138768 A138769 A138770
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KEYWORD
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nonn,tabf
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2008
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