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Search: id:A086646
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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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7
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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
(list; table; graph; listen)
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OFFSET
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0,4
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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) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 26 2004
Sum_{k, 0<=k<=n} T(n, k)*(-4)^k*9^(n-k) = A002438(n+1) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 26 2005
Sum_{k, 0<=k<=n}(-1)^k*9^(n-k)*T(n,k)=A000436(n) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 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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CROSSREFS
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Cf. A000364 A005647 A085938.
Cf. A000281.
Row sums : A000795.
Adjacent sequences: A086643 A086644 A086645 this_sequence A086647 A086648 A086649
Sequence in context: A105577 A054655 A086745 this_sequence A113106 A060011 A021068
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jul 26 2003
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