= Use data files (if available)

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Syntax Transforms ADD(A, k): a'[n] = a[n] + k add constant ALT(A): a'[n] = (-1)^n * a[n] shift sign of every second element BIN(a): a'[n] = Sum_{k<=n} ((n k) * a[k]) binomial transform CON(A): a'[n] = Sum_{k<=n} (a[k] * a[n-k]) self-convolution CPROD(A): a'[n] = a[n] * a[n+1] product of two consecutive elements DIFF(A): a'[n] = a[n+1] - a[n] first differences DIV(A, k): a'[n] = floor(a[n] / k) divide by constant EULER(A): euler transform IBIN(a): a'[n] = Sum_{k<=n} ((-1)^k * (n k) * a[k]) inverse binomial transform IMOEB(A): a'[n] = Sum_{d|n} (a[d]) inverse moebius transform MOEB(A): a'[n] = Sum_{d|n} (mu(n/d) * a[d]) moebius transform MUL(A, k): a'[n] = a[n] * k multiply with constant PRODS(n): a'[n] = Product_{k<=n} (a[k]) partial products SHIFT(A, k): a'[n] = a[n+k] shift index SSUMS(A): a'[n] = Sum_{k<=n} (a[k]^2) partial sums of squares STIR1(A) a'[n] = Sum_{k<=n} (s(n, k) * a[n-k]) first stirling transform STIR2(A) a'[n] = Sum_{k<=n} (S(n, k) * a[n-k]) second stirling transform SUB(A, B) a'[n] = a[n] - k substract constant SUMS(A): a'[n] = Sum_{k<=n} (a[k]) partial sums WSUMS(A): a'[n] = Sum_{k<=n} (k * a[k]) linear weighted partial sums Binary Operations ADD(A, B) a'[n] = a[n] + b[n] add elements DIR(A, B) a'[n] = Sum_{d|n} (a[d] * b[n/d]) dirichlet convolution DOT(A, B) a'[n] = a[n] * b[n] dot product SUB(A, B) a'[n] = a[n] - b[n] substract elements