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 A119580 a(n) = (n^2+n^3)*binomial(2*n,n). 0
 0, 4, 72, 720, 5600, 37800, 232848, 1345344, 7413120, 39382200, 203231600, 1024287264, 5062180032, 24607819600, 117942804000, 558423072000, 2615901857280, 12139419556440, 55866532906800, 255192804636000, 1157910842088000, 5222177897816880, 23422829664131040 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..22. FORMULA From Amiram Eldar, Aug 28 2022: (Start) a(n) = (n*(n+1))^2*A000108(n). Sum_{n>=1} 1/a(n) = Pi/sqrt(3) - Pi^2/18 - 1. Sum_{n>=1} (-1)^(n+1)/a(n) = 6*log(phi)^2 - 2*sqrt(5)*log(phi) + 1, where phi is the golden ratio (A001622). (End) a(n) = A000984(n)*A011379(n). - Michel Marcus, Aug 28 2022 MAPLE [seq ((n^2+n^3)*(binomial(2*n, n)), n=0..29)]; MATHEMATICA Table[(n^2 + n^3) * Binomial[2 n, n], {n, 0, 30}] (* Wesley Ivan Hurt, Feb 26 2014 *) CROSSREFS Cf. A000108, A000984, A001622, A011379. Sequence in context: A003752 A062018 A192830 * A209539 A139745 A066992 Adjacent sequences: A119577 A119578 A119579 * A119581 A119582 A119583 KEYWORD easy,nonn AUTHOR Zerinvary Lajos, May 31 2006 STATUS approved

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Last modified April 13 11:55 EDT 2024. Contains 371640 sequences. (Running on oeis4.)