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 A118191 Row sums of triangle A118190: a(n) = Sum_{k=0..n} (5^k)^(n-k) for n>=0. 3
 1, 2, 7, 52, 877, 32502, 2740627, 507843752, 214111484377, 198376465625002, 418186492923828127, 1937270172119160156252, 20419262349796295263671877, 472966350615029335022460937502, 24925857360591180741786959228515627 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Self-convolution of A118195; in general, sqrt(Sum_{n>=0} x^n/(1-q^n*x)) is an integer series whenever q == 1 (mod 4). Also equals column 0 of the matrix square of triangle A118190, where [A118190^2](n,k) = a(n-k)*(5^k)^(n-k) for n>=k>=0. LINKS FORMULA G.f.: A(x) = Sum_{n>=0} x^n/(1-5^n*x). EXAMPLE A(x) = 1/(1-x) + x/(1-5x) + x^2/(1-25x) + x^3/(1-125x) + ... = 1 + 2*x + 7*x^2 + 52*x^3 + 877*x^4 + 32502*x^5 + ... PROG (PARI) a(n)=sum(k=0, n, (5^k)^(n-k)) CROSSREFS Cf. A118190 (triangle), A118195 (A(x)^(1/2)), A118192 (antidiagonal sums). Sequence in context: A046662 A237195 A275597 * A005588 A106898 A106899 Adjacent sequences:  A118188 A118189 A118190 * A118192 A118193 A118194 KEYWORD nonn AUTHOR Paul D. Hanna, Apr 15 2006 STATUS approved

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Last modified February 25 08:21 EST 2020. Contains 332221 sequences. (Running on oeis4.)