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A361607 a(n) = n! * Sum_{k=0..n} binomial(n+(n-1)*k,n*k)/k!. 2
1, 2, 9, 88, 1457, 35226, 1158097, 49554464, 2664907233, 175012404562, 13725980234201, 1263867766626312, 134795551989905809, 16464112185873351338, 2280346417134518709537, 355060682992984062716176 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = n! * [x^n] exp( x/(1-x)^n ) / (1-x).
a(n) = Sum_{k=0..n} (n*k+n-k)!/(n*k)! * binomial(n,k).
log(a(n)) ~ n*(2*log(n) - log(log(n)) - 1 - log(2) + (log(log(n)) + log(2) + 1/2)/log(n)). - Vaclav Kotesovec, Mar 17 2023
MATHEMATICA
Table[Sum[Binomial[n, k]*(n*k + n - k)!/(n*k)!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 17 2023 *)
PROG
(PARI) a(n) = sum(k=0, n, (n*k+n-k)!/(n*k)!*binomial(n, k));
CROSSREFS
Main diagonal of A361600.
Cf. A293013.
Sequence in context: A347013 A132431 A228509 * A001192 A006120 A012941
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 17 2023
STATUS
approved

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Last modified April 21 16:35 EDT 2024. Contains 371874 sequences. (Running on oeis4.)