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 A121676 a(n) = [x^n] (1 + x*(1+x)^(n-1) )^(n+1). 4
 1, 2, 6, 32, 250, 2412, 27524, 360600, 5296050, 85805420, 1515794467, 28926900312, 591903009295, 12907255696636, 298428274844730, 7284351640977920, 187013495992710210, 5033669346061547724, 141643700005223732471 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) is divisible by (n+1): a(n)/(n+1) = A121677(n). LINKS Table of n, a(n) for n=0..18. 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)^3 )^5 = 250, since (1 + x*(1+x)^3 )^5 = 1 + 5*x + 25*x^2 + 85*x^3 + 250*x^4 +... PROG (PARI) a(n)=sum(k=0, n+1, binomial(n+1, k)*binomial((n-1)*k, n-k)) CROSSREFS Cf. A121677; variants: A121673-A121675, A121678-A121680. Sequence in context: A211195 A346452 A012324 * A326096 A346270 A133596 Adjacent sequences: A121673 A121674 A121675 * A121677 A121678 A121679 KEYWORD nonn AUTHOR Paul D. Hanna, Aug 15 2006 STATUS approved

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Last modified February 27 16:21 EST 2024. Contains 370378 sequences. (Running on oeis4.)