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A121675 a(n) = [x^n] (1 + x*(1+x)^(n+1) )^n. 3
1, 1, 7, 43, 371, 3926, 47622, 654151, 9999523, 167557174, 3046387103, 59616689595, 1247357472869, 27747682830531, 653192297754076, 16206706672425167, 422358302959175123, 11526119161103900834 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..n} C(n,k) * C((n+1)*k,n-k).
EXAMPLE
At n=4, a(4) = [x^4] (1 + x*(1+x)^5 )^4 = 371, since
(1 + x*(1+x)^5 )^4 = 1 + 4*x + 26*x^2 + 104*x^3 + 371*x^4 +...
MATHEMATICA
Table[Sum[Binomial[n, k] * Binomial[(n+1)*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+1)*k, n-k))
CROSSREFS
Cf. variants: A121673, A121674, A121676-A121680.
Sequence in context: A164775 A127999 A208595 * A243273 A292502 A294361
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 15 2006
STATUS
approved

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Last modified April 17 17:01 EDT 2024. Contains 371765 sequences. (Running on oeis4.)