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 A121680 a(n) = [x^n] (1 + x*(1+x)^(n+1) )^(n+1). 8
 1, 2, 12, 76, 655, 6816, 81690, 1109816, 16782399, 278438740, 5016899833, 97368894756, 2021749249403, 44658312247290, 1044437050070340, 25757381769393392, 667470006331599523, 18119105978249333988 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) is divisible by (n+1): a(n)/(n+1) = A121681(n). LINKS Table of n, a(n) for n=0..17. FORMULA a(n) = Sum_{k=0..n+1} C(n+1,k) * C((n+1)*k,n-k). EXAMPLE At n=4, a(4) = [x^4] (1 + x*(1+x)^5 )^5 = 655, since (1 + x*(1+x)^5 )^5 = 1 + 5*x + 35*x^2 + 160*x^3 + 655*x^4 +... MATHEMATICA Table[Sum[Binomial[n+1, k] * Binomial[(n+1)*k, n-k], {k, 0, n+1}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 02 2020 *) PROG (PARI) a(n)=sum(k=0, n+1, binomial(n+1, k)*binomial((n+1)*k, n-k)) CROSSREFS Cf. A121681; variants: A121673-A121679. Sequence in context: A037620 A198474 A285489 * A277478 A081014 A223771 Adjacent sequences: A121677 A121678 A121679 * A121681 A121682 A121683 KEYWORD nonn AUTHOR Paul D. Hanna, Aug 15 2006 STATUS approved

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Last modified April 16 10:08 EDT 2024. Contains 371698 sequences. (Running on oeis4.)