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A121674 a(n) = [x^n] (1 + x*(1+x)^n )^n. 3
1, 1, 5, 28, 233, 2376, 28102, 379016, 5707025, 94439440, 1699067321, 32951077193, 684009742319, 15110032165151, 353485501643471, 8721374385748256, 226128389777924385, 6142306518887606112, 174311816444805024379 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..n} C(n,k) * C(n*k,n-k).
EXAMPLE
At n=4, a(4) = [x^4] (1 + x*(1+x)^4 )^4 = 233, since
(1 + x*(1+x)^4 )^4 = 1 + 4*x + 22*x^2 + 76*x^3 + 233*x^4 +...
MATHEMATICA
Table[Sum[Binomial[n, k] * Binomial[n*k, n-k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jun 12 2015 *)
PROG
(PARI) a(n)=sum(k=0, n, binomial(n, k)*binomial(n*k, n-k))
CROSSREFS
Cf. variants: A121673, A121675-A121680.
Sequence in context: A038172 A183375 A000530 * A306181 A362690 A116977
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 15 2006
STATUS
approved

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Last modified April 20 09:04 EDT 2024. Contains 371799 sequences. (Running on oeis4.)