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A121676 a(n) = [x^n] (1 + x*(1+x)^(n-1) )^(n+1). 4
1, 2, 6, 32, 250, 2412, 27524, 360600, 5296050, 85805420, 1515794467, 28926900312, 591903009295, 12907255696636, 298428274844730, 7284351640977920, 187013495992710210, 5033669346061547724, 141643700005223732471 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(n) is divisible by (n+1): a(n)/(n+1) = A121677(n).
LINKS
FORMULA
a(n) = Sum_{k=0..n+1} C(n+1,k) * C((n-1)*k,n-k).
EXAMPLE
At n=4, a(4) = [x^4] (1 + x*(1+x)^3 )^5 = 250, since
(1 + x*(1+x)^3 )^5 = 1 + 5*x + 25*x^2 + 85*x^3 + 250*x^4 +...
PROG
(PARI) a(n)=sum(k=0, n+1, binomial(n+1, k)*binomial((n-1)*k, n-k))
CROSSREFS
Sequence in context: A211195 A346452 A012324 * A326096 A346270 A133596
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 15 2006
STATUS
approved

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Last modified February 27 16:21 EST 2024. Contains 370378 sequences. (Running on oeis4.)