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A086646
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Triangle, read by rows, of numbers T(n; k), 0<=k<=n, given by T(n; k) = A000364(n-k)*binomial(2*n; 2*k).
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8
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1, 1, 1, 5, 6, 1, 61, 75, 15, 1, 1385, 1708, 350, 28, 1, 50521, 62325, 12810, 1050, 45, 1, 2702765, 3334386, 685575, 56364, 2475, 66, 1, 199360981, 245951615, 50571521, 4159155, 183183, 5005, 91, 1, 19391512145, 23923317720, 4919032300, 404572168
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OFFSET
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0,4
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COMMENTS
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The elements of the matrix inverse are apparently given by T^(-1)(n,k) = (-1)^(n+k)*A086645(n,k). - R. J. Mathar, Mar 14 2013
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LINKS
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Table of n, a(n) for n=0..39.
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FORMULA
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cosh(u*t)/cos(t) = Sum(n>=0, S_2n(u)*(t^(2*n))*(1/(2*n)!). S_2n(u) = Sum(k>=0, T(n; k)*u^(2*k)). Sum(k>=0, (-1)^k*T(n; k) = 0 . Sum(k>=0, T(n; k) = 2^n*A005647(n); A005647 : Salie numbers.
Triangle T(n, k) read by rows; given by [1, 4, 9, 16, 25, 36, 49, ...] DELTA [1, 0, 1, 0, 1, 0, 1, 0, 1, ...] where DELTA is the operator defined in A084938.
Sum_{k=0..n} (-1)^k*T(n, k)*4^(n-k)= A000281(n) . - Philippe Deléham, Jan 26 2004
Sum_{k, 0<=k<=n} T(n, k)*(-4)^k*9^(n-k) = A002438(n+1) . - Philippe DELEHAM, Aug 26 2005
Sum_{k, 0<=k<=n}(-1)^k*9^(n-k)*T(n,k)=A000436(n) . - Philippe DELEHAM, Oct 27 2006
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EXAMPLE
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1;
1, 1;
5, 6, 1;
61, 75, 15, 1;
1385, 1708, 350, 28, 1;
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MAPLE
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A086646 := proc(n, k)
if k < 0 or k > n then
0 ;
else
A000364(n-k)*binomial(2*n, 2*k) ;
end if;
end proc: # R. J. Mathar, Mar 14 2013
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CROSSREFS
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Cf. A000364 A005647 A084938.
Cf. A000281.
Row sums : A000795.
Sequence in context: A105577 A054655 A086745 * A181612 A216808 A113106
Adjacent sequences: A086643 A086644 A086645 * A086647 A086648 A086649
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Philippe Deléham, Jul 26 2003
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STATUS
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approved
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