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Search: id:A109692
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| A109692 |
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Triangle of coefficients in expansion of (1+x)(1+3x)(1+5x)(1+7x)...(1+(2n-1)x). |
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8
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| 1, 1, 1, 1, 4, 3, 1, 9, 23, 15, 1, 16, 86, 176, 105, 1, 25, 230, 950, 1689, 945, 1, 36, 505, 3480, 12139, 19524, 10395, 1, 49, 973, 10045, 57379, 177331, 264207, 135135, 1, 64, 1708, 24640, 208054, 1038016, 2924172, 4098240, 2027025, 1, 81, 2796, 53676
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Triangle T(n,k),0<=k<=n, read by rows, given by [1, 0, 1, 0, 1, 0, 1, 0, 1, ...] DELTA [1, 2, 3, 4, 5, 6, 7, 8, 9, ...] where DELTA is the operator defined in A084938.
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FORMULA
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Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 08 2009: (Start)
a(n, m) = a(n-1,m)+(2*n-1)*a(n-1,m-1) with a(n, n) = (2*n-1)!! and a(n, 0) = 1.
(End)
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EXAMPLE
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1; 1, 1; 1, 4, 3; 1, 9, 23, 15; 1, 16, 86, 176, 105; ...
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MAPLE
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Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 08 2009: (Start)
nmax:=8; mmax:=nmax: for n from 0 to nmax do a(n, 0):=doublefactorial(2*n-1) od: for n from 0 to nmax do a(n, n):=1 od: for n from 2 to nmax do for m from 1 to n-1 do a(n, m) := (2*n-1)*a(n-1, m)+a(n-1, m-1) od; od: T:=0; for n from 0 to nmax do for m from 0 to n do a(T):=a(n, n-m); T:=T+1 od: od: seq(a(n), n=0..T-1);
(End)
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CROSSREFS
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A039758 is signed version. A028338 transposed.
Diagonals : A000012, A000290, A024196, A024197, A024198; A001147, A004041, A028339, A028340, A028341 . Row sums : A000165.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 08 2009: (Start)
A161198 is a transposed scaled triangle version.
(End)
Sequence in context: A165732 A123160 A039758 this_sequence A157894 A128813 A109062
Adjacent sequences: A109689 A109690 A109691 this_sequence A109693 A109694 A109695
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KEYWORD
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nonn,tabl
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 08 2005
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