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 A061188 Triangle of coefficients of polynomials (rising powers) useful for convolutions of A000032(n+1), n >= 0 (Lucas numbers). 2
 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; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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). LINKS Table of n, a(n) for n=0..29. EXAMPLE {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). CROSSREFS A061189(n, m) (companion triangle), A060922(n, m) (Lucas convolution triangle). Sequence in context: A363695 A228168 A178977 * A033429 A168011 A160749 Adjacent sequences: A061185 A061186 A061187 * A061189 A061190 A061191 KEYWORD nonn,tabl AUTHOR Wolfdieter Lang, Apr 20 2001 STATUS approved

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Last modified November 30 23:40 EST 2023. Contains 367464 sequences. (Running on oeis4.)