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A121678 a(n) = [x^n] (1 + x*(1+x)^n )^(n+1). 3
1, 2, 9, 52, 425, 4236, 49294, 655096, 9731313, 159114880, 2832245911, 54400757016, 1119436524947, 24532373640334, 569732648555295, 13962373137304496, 359767723241891425, 9715902692094061488 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(n) is divisible by (n+1): a(n)/(n+1) = A121679(n).
LINKS
FORMULA
a(n) = Sum_{k=0..n+1} C(n+1,k) * C(n*k,n-k).
EXAMPLE
At n=5, a(5) = [x^5] (1 + x*(1+x)^5)^6 = 4236, since
(1+x*(1+x)^5)^6 = 1 + 6*x + 45*x^2 + 230*x^3 + 1050*x^4 + 4236*x^5 +...
PROG
(PARI) a(n)=sum(k=0, n+1, binomial(n+1, k)*binomial(n*k, n-k))
CROSSREFS
Cf. A121679; variants: A121673-A121676, A121680.
Sequence in context: A369090 A110322 A161631 * A124347 A360743 A360193
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 15 2006
STATUS
approved

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Last modified April 16 08:27 EDT 2024. Contains 371698 sequences. (Running on oeis4.)