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A103212 a(n) = (1/n) * Sum_{i=0..n-1} C(n,i)*C(n,i+1)*(n-1)^i*n^(n-i) for n>=1, a(0)=1. 2
1, 1, 6, 93, 2380, 85405, 3956106, 224939113, 15175702200, 1185580310121, 105302043709390, 10482085765658661, 1156062800841590148, 139945327558704629221, 18449221488652046992914, 2631255715262150125502865, 403689862107153669227378416, 66297391981691913179574751633 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = A103209(n, n-1). [corrected by Vaclav Kotesovec, Sep 24 2017]
a(n) ~ 2^(2*n) * n^(n-3/2) / (sqrt(Pi) * exp(1/2)). - Vaclav Kotesovec, Sep 24 2017
MATHEMATICA
Table[HypergeometricPFQ[{-n, n+1}, {2}, -n+1], {n, 0, 20}] (* Vaclav Kotesovec, Sep 24 2017 *)
Flatten[{1, 1, Table[Sum[Binomial[n, k]*Binomial[n, k+1]*(n-1)^k*n^(n-k), {k, 0, n-1}]/n, {n, 2, 20}]}] (* Vaclav Kotesovec, Sep 24 2017 *)
PROG
(PARI) a(n) = {if(n==0, 1, sum(i=0, n-1, binomial(n, i)*binomial(n, i+1)*(n-1)^i*n^(n-i))/n)} \\ Andrew Howroyd, Apr 14 2021
CROSSREFS
Sequence in context: A331623 A158121 A328427 * A359928 A033935 A218682
KEYWORD
nonn
AUTHOR
Ralf Stephan, Jan 27 2005
EXTENSIONS
Prepended a(0)=1 from Vaclav Kotesovec, Sep 24 2017
Terms a(15) and beyond from Andrew Howroyd, Apr 14 2021
STATUS
approved

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Last modified July 16 08:10 EDT 2024. Contains 374345 sequences. (Running on oeis4.)