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Search: id:A061189
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| A061189 |
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Triangle of coefficients of polynomials (rising powers) useful for convolutions of A000204(n+1), n >= 0 (Lucas numbers). |
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3
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| 1, 2, 0, -10, 15, 25, 30, 475, 450, 125, 6000, 8500, 6250, 5000, 1250, 96000, 146250, 189375, 159375, 65625, 9375, 180000, 5355000, 8881250, 5578125, 2515625, 721875, 78125, 44100000, 254700000, 341775000
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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The row polynomials pL2(n,x) := sum(a(n,m)*x^m,m=0..n) and pL1(n,x) := sum(A061188(n,m)*x^m,m=0..n) appear in the k-fold convolution of the Lucas numbers L(n+1)= A000204(n+1)= A000032(n+1), n >= 0, as follows: L(k; n) := A060922(n+k,k)= (pL1(k,n)*L(n+2)+pL2(k,n)*L(n+1)/(k!*5^k).
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EXAMPLE
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{1}; {2,0}; {-10,15,25}; {30,475,450,125}; ...; pL2(2,n)=5*(-2+3*n+5*n^2)= 5*(1+n)*(-2+5*n).
L(2; n) := A060922(n+2,2)= A060929(n) = (1+n)*((4+5*n)*L(n+2)+(-2+5*n)*L(n+1))/(2*5).
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CROSSREFS
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A061188(n, m) (companion triangle), A060922(n, m) (Lucas convolution triangle).
Sequence in context: A037996 A002741 A070681 this_sequence A019220 A019140 A086890
Adjacent sequences: A061186 A061187 A061188 this_sequence A061190 A061191 A061192
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KEYWORD
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sign,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Apr 20 2001
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