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 A117937 Triangle, rows = inverse binomial transforms of A117938 columns. 4
 1, 1, 1, 3, 3, 2, 4, 10, 12, 6, 7, 27, 58, 60, 24, 11, 71, 240, 420, 360, 120, 18, 180, 920, 2460, 3504, 2520, 720, 29, 449, 3360, 13020, 27720, 32760, 20160, 5040, 47, 1107, 11898, 64620, 194184, 337680, 338400, 181440, 40320, 76, 2710, 41268, 307194, 1257120, 3029760, 4415040 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A117936 is the companion triangle using analogous Fibonacci polynomials. Left border of A117936 = the Lucas numbers; right border = factorials. [Note that most of the comments here and in many related sequences by the same author refer to some unusual definition of binomial transforms for sequences starting at index 1. - R. J. Mathar, Jul 05 2012] LINKS Table of n, a(n) for n=1..52. FORMULA Rows of the triangle are inverse binomial transforms of A117938 columns. A117938 columns are generated from f(x), Lucas polynomials: (1); (x); (x^2 + 2); (x^3 + 3x); (x^4 + 4x + 2);... EXAMPLE First few rows of the triangle are: 1; 1, 1; 3, 3, 2; 4, 10, 12, 6; 7, 27, 58, 60, 24; 11, 71, 240, 420, 360, 120; ... For example, row 4: (4, 10, 12, 6) = the inverse binomial transform of column 4 of A117938: (4, 14, 36, 76, 140...), being f(x), x =1,2,3...using the Lucas polynomial x^3 + 3x. MAPLE A117937 := proc(n, k) add( A117938(n+i, n)*binomial(k-1, i)*(-1)^(1+i-k), i=0..k-1) ; end proc: seq(seq(A117937(n, k), k=1..n), n=1..13) ; # R. J. Mathar, Aug 16 2019 CROSSREFS Cf. A117936, A117938. Sequence in context: A050610 A151848 A238238 * A110897 A116644 A166462 Adjacent sequences: A117934 A117935 A117936 * A117938 A117939 A117940 KEYWORD nonn,tabl,easy AUTHOR Gary W. Adamson, Apr 04 2006 STATUS approved

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Last modified September 29 23:48 EDT 2023. Contains 365781 sequences. (Running on oeis4.)