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 A243923 Row sums of triangle A243920. 3
 0, 1, 4, 12, 57, 469, 5409, 77321, 1304086, 25263208, 551790014, 13398776948, 357740951660, 10409057421898, 327640162774856, 11087710302096702, 401290657576717001, 15462394004585328685, 631795378164538352085, 27280160237622374011469, 1240933576265292837746859 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Triangle T = A243920 is generated by sums of matrix powers of itself such that: T(n,k) = Sum_{j=1..n-k-1} [T^j](n-1,k) with T(n+1,n) = 2*n+1 and T(n,n)=0 for n>=0. Also, column k of triangle T = A243920 obeys the rule: (2*k+1)*x^(k+1) = Sum_{n>=0} T(n,k) * x^n * (1-x)^(n-k) / Product_{j=k+1..n-1} (1+2*j*x). LINKS Table of n, a(n) for n=0..20. EXAMPLE Equals rows sums of triangle T = A243920, which begins: 0; 1, 0; 1, 3, 0; 4, 3, 5, 0; 27, 18, 5, 7, 0; 254, 159, 40, 7, 9, 0; 3048, 1836, 435, 70, 9, 11, 0; 44328, 26028, 5930, 903, 108, 11, 13, 0; ... such that T as an infinite triangular matrix satisfies: [I - T]^(-1) = Sum_{n>=0} T^n and equals T shifted up 1 row (with all '1's replacing the main diagonal): 1; 1, 1; 4, 3, 1; 27, 18, 5, 1; 254, 159, 40, 7, 1; 3048, 1836, 435, 70, 9, 1; 44328, 26028, 5930, 903, 108, 11, 1; ... PROG (PARI) /* Get row sums using the g.f. for columns in triangle A243920: */ {A243920(n, k)=if(n

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Last modified April 21 09:27 EDT 2024. Contains 371851 sequences. (Running on oeis4.)