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 A210438 G.f.: Sum_{n>=0} x^n * Product_{k=1..n} (k^2 + x) / (1 + k^2*x + x^2). 2
 1, 1, 4, 20, 174, 2262, 40894, 980590, 30095022, 1149982990, 53521460958, 2980006437662, 195562339712590, 14936971352026094, 1313606920832545022, 131776096083434471678, 14956389843996883667182, 1906794751364126563388238, 271321222225812454677233694 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Compare to the identity: Sum_{n>=0} x^n * Product_{k=1..n} (k + x) / (1 + k*x + x^2) = (1+x^2)/(1-x). LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..220 FORMULA a(n) ~ 2^(2*n+5) * n^(2*n+5/2) / (exp(2*n) * Pi^(2*n+3/2)). - Vaclav Kotesovec, Nov 02 2014 EXAMPLE G.f.: A(x) = 1 + x + 4*x^2 + 20*x^3 + 174*x^4 + 2262*x^5 + 40894*x^6 +... where A(x) = 1 + x*(1+x)/(1+x+x^2) + x^2*(1+x)*(4+x)/((1+x+x^2)*(1+4*x+x^2)) + x^3*(1+x)*(4+x)*(9+x)/((1+x+x^2)*(1+4*x+x^2)*(1+9*x+x^2)) + x^4*(1+x)*(4+x)*(9+x)*(16+x)/((1+x+x^2)*(1+4*x+x^2)*(1+9*x+x^2)*(1+16*x+x^2)) +... PROG (PARI) {a(n)=polcoeff( sum(m=0, n, x^m*prod(k=1, m, (k^2+x)/(1+k^2*x+x^2 +x*O(x^n))) ), n)} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A209778, A221370. Sequence in context: A366639 A068965 A185672 * A054474 A364344 A368455 Adjacent sequences: A210435 A210436 A210437 * A210439 A210440 A210441 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 19 2013 STATUS approved

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Last modified June 12 14:48 EDT 2024. Contains 373331 sequences. (Running on oeis4.)