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A361829
a(n) = Sum_{k=0..n} binomial(2*k,k) * binomial(n*k,n-k).
3
1, 2, 10, 62, 486, 4482, 47106, 553226, 7152438, 100644194, 1527758136, 24839853326, 430045385424, 7888706328934, 152685931935634, 3106864307092950, 66253232332628166, 1476558925897693698, 34307420366092350048, 829217371825336147142
OFFSET
0,2
FORMULA
a(n) = [x^n] 1/sqrt(1 - 4*x*(1+x)^n).
log(a(n)) ~ n*(log(n) + (2*log(2) - 1)/log(n) - (1 - 1/log(n))*log(log(n) - 1)). - Vaclav Kotesovec, Mar 26 2023
MATHEMATICA
Table[Sum[Binomial[2*k, k]*Binomial[n*k, n-k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 26 2023 *)
PROG
(PARI) a(n) = sum(k=0, n, binomial(2*k, k)*binomial(n*k, n-k));
CROSSREFS
Main diagonal of A361830.
Sequence in context: A307364 A141140 A232472 * A361494 A371546 A175962
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 26 2023
STATUS
approved