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A121677 a(n) = A121676(n)/(n+1) = [x^n] (1 + x*(1+x)^(n-1) )^(n+1) / (n+1). 1
1, 1, 2, 8, 50, 402, 3932, 45075, 588450, 8580542, 137799497, 2410575026, 45531000715, 921946835474, 19895218322982, 455271977561120, 11000793881924130, 279648297003419318, 7454931579222301709 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..n+1} C(n+1,k) * C((n-1)*k,n-k) / (n+1).
EXAMPLE
At n=4, a(4) = [x^4] (1 + x*(1+x)^3 )^5/5 = 250/5 = 50, since
(1 + x*(1+x)^3 )^5 = 1 + 5*x + 25*x^2 + 85*x^3 + 250*x^4 +...
MATHEMATICA
Flatten[{1, Table[Sum[Binomial[n+1, k] * Binomial[(n-1)*k, n-k] / (n+1), {k, 0, n+1}], {n, 1, 20}]}] (* Vaclav Kotesovec, Jun 12 2015 *)
PROG
(PARI) a(n)=sum(k=0, n+1, binomial(n+1, k)*binomial((n-1)*k, n-k))/(n+1)
CROSSREFS
Sequence in context: A231352 A186182 A274273 * A120956 A000557 A193352
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 15 2006
STATUS
approved

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Last modified March 2 17:21 EST 2024. Contains 370497 sequences. (Running on oeis4.)