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 A099237 a(n) = Sum_{k=0..n} binomial(n*(n-k), k). 4
 1, 1, 3, 10, 45, 251, 1624, 11908, 97545, 880660, 8664546, 92096731, 1050304775, 12778138842, 165033693175, 2253204163256, 32401745953105, 489207829112931, 7733130368443057, 127664099576228184, 2196149923000824756 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Main diagonal of A099233. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..490 FORMULA From Vaclav Kotesovec, Feb 19 2018: (Start) a(n)^(1/n) ~ n^(n/w) * (n+1-w)^(1 - (n+1)/w) * (w-1)^(1/w - 1), where w = LambertW(exp(1)*n), a(n)^(1/n) ~ n/log(n), but the convergence is too slow. (End) MAPLE A099237:= n-> add( binomial(n*j, n-j), j=0..n ); seq(A099237(n), n=0..30); # G. C. Greubel, Mar 09 2021 MATHEMATICA Table[Sum[Binomial[n*(n - k), k], {k, 0, n}], {n, 0, 30}] (* Vaclav Kotesovec, Feb 19 2018 *) PROG (Sage) def A099237(n): return sum( binomial(n*j, n-j) for j in (0..n)) [A099237(n) for n in (0..30)] # G. C. Greubel, Mar 09 2021 (Magma) A099237:= func< n | (&+[Binomial(n*j, n-j): j in [0..n]]) >; [A099237(n): n in [0..30]]; // G. C. Greubel, Mar 09 2021 CROSSREFS Cf. A099233, A157114. Sequence in context: A184947 A330250 A207652 * A006220 A020026 A077002 Adjacent sequences:  A099234 A099235 A099236 * A099238 A099239 A099240 KEYWORD easy,nonn AUTHOR Paul Barry, Oct 08 2004 STATUS approved

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Last modified June 21 10:09 EDT 2021. Contains 345360 sequences. (Running on oeis4.)