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 A134082 Triangle read by rows, (n-1) zeros followed by (2n, 1). 9
 1, 2, 1, 0, 4, 1, 0, 0, 6, 1, 0, 0, 0, 8, 1, 0, 0, 0, 0, 10, 1, 0, 0, 0, 0, 0, 12, 1, 0, 0, 0, 0, 0, 0, 14, 1, 0, 0, 0, 0, 0, 0, 0, 16, 1, 0, 0, 0, 0, 0, 0, 0, 0, 18, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A134082 * [1,2,3,...] = A084849: (1, 4, 11, 22, 37, ...). Binomial transform of A134082 = A134083. A112295 replaces subdiagonal with (-1,-3,-5, ...). LINKS G. C. Greubel, Rows n = 0..50 of the triangle, flattened FORMULA Triangle read by rows, (n-1) zeros followed by (2n, 1). As an infinite lower triangular matrix, (1,1,1,...) in the main diagonal and (2,4,6,8,...) in the subdiagonal. From formalism in A132382, e.g.f. = I_o[2*(u*x)^(1/2)] (1+2x) where I_o is the zeroth modified Bessel function of the first kind, i.e., I_o[2*(u*x)^(1/2)] = Sum_{j>=0} u^j/j! * x^j/j!. - Tom Copeland, Dec 07 2007 Row polynomial e.g.f.: exp(x*y)(1+2x). - Tom Copeland, Dec 03 2013 Sum_{k=0..n} T(n,k) = 2*n+1 = A005408(n). - G. C. Greubel, Feb 17 2021 EXAMPLE First few rows of the triangle: 1; 2, 1; 0, 4, 1; 0, 0, 6, 1; 0, 0, 0, 8, 1; 0, 0, 0, 0, 10, 1; ... MATHEMATICA T[n_, k_]:= If[k==n, 1, If[k==n-1, 2*n, 0]]; Table[T[n, k], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Feb 17 2021 *) PROG (Sage) def A134082(n, k): return 1 if k==n else 2*n if k==n-1 else 0 flatten([[A134082(n, k) for k in (0..n)] for n in (0..15)]) # G. C. Greubel, Feb 17 2021 (Magma) A134082:= func< n, k | k eq n select 1 else k eq n-1 select 2*n else 0 >; [A134082(n, k): k in [0..n], n in [0..15]]; // G. C. Greubel, Feb 17 2021 CROSSREFS Cf. A005408, A084849, A112295, A134083. Sequence in context: A053117 A121448 A019094 * A185740 A139360 A326759 Adjacent sequences: A134079 A134080 A134081 * A134083 A134084 A134085 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Oct 07 2007 EXTENSIONS More terms added by G. C. Greubel, Feb 17 2021 STATUS approved

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Last modified September 29 16:13 EDT 2023. Contains 365773 sequences. (Running on oeis4.)