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Search: id:A061188
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| A061188 |
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Triangle of coefficients of polynomials (rising powers) useful for convolutions of A000032(n+1), n >= 0 (Lucas numbers). |
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+0
3
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| 0, 1, 5, 20, 45, 25, 240, 350, 600, 250, 3000, 9250, 13125, 8750, 1875, 93000, 373750, 361875, 240625, 103125, 15625, 3690000, 11077500, 12818750, 8531250, 4156250, 1181250, 125000, 116550000, 312037500
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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The row polynomials pL1(n,x) := sum(a(n,m)*x^m,m=0..n) and pL2(n,x) := sum(A061189(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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{0}; {1,5}; {20,45,25}; {240,350,600,250}; ...; pL1(2,n)=5*(4+9*n+5*n^2)= 5*(1+n)*(4+5*n).
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CROSSREFS
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A061189(n, m) (companion triangle), A060922(n, m) (Lucas convolution triangle).
Sequence in context: A031082 A161445 A031304 this_sequence A033429 A147002 A005287
Adjacent sequences: A061185 A061186 A061187 this_sequence A061189 A061190 A061191
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KEYWORD
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nonn,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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