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 A336522 a(n) is the coefficient of x^(n^2) in expansion of ( (1 + x)/(1 - x) )^n. 3
 1, 2, 16, 326, 11008, 525002, 32497680, 2478629134, 224921989120, 23681262354194, 2838826197080080, 381825269929428822, 56949892477659339520, 9329658433405643973850, 1665421971238565711337488, 321771059958076157377283102, 66901218825369170336327860224, 14894388013750938445628478094370 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..311 FORMULA a(n) = (1/n) * [x^n] ( (1 + x)/(1 - x) )^(n^2) for n > 0. a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n^2+k-1,n-1). a(n) = (1/n) * Sum_{k=0..n} binomial(n^2,n-k) * binomial(n^2+k-1,k) for n > 0. a(n) = Sum_{k=1..n} 2^k * binomial(n,k) * binomial(n^2-1,k-1) for n > 0. a(n) ~ 2^(n - 1/2) * exp(n) * n^(n - 3/2) / sqrt(Pi). - Vaclav Kotesovec, Jul 31 2021 MATHEMATICA a[n_] := Sum[Binomial[n, k] * Binomial[n^2 + k - 1, n - 1], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Jul 24 2020 *) PROG (PARI) {a(n) = if(n==0, 1, sum(k=0, n, binomial(n^2, n-k) * binomial(n^2+k-1, k))/n)} (PARI) {a(n) = if(n==0, 1, sum(k=1, n, 2^k*binomial(n, k) * binomial(n^2-1, k-1)))} CROSSREFS Main diagonal of A336521. Cf. A336537. Sequence in context: A278589 A171212 A282392 * A294039 A009100 A009109 Adjacent sequences: A336519 A336520 A336521 * A336523 A336524 A336525 KEYWORD nonn AUTHOR Seiichi Manyama, Jul 24 2020 STATUS approved

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Last modified September 24 22:14 EDT 2023. Contains 365582 sequences. (Running on oeis4.)