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A121673 a(n) = [x^n] (1 + x*(1+x)^(n-1) )^n. 8
1, 1, 3, 16, 131, 1306, 15257, 203967, 3047907, 50115310, 896746169, 17308420306, 357767229778, 7872926416538, 183537476164902, 4513828442107368, 116688468769638435, 3160881019508153238, 89471871451166037425 (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)^3 )^4 = 131, since
(1 + x*(1+x)^3 )^4 = 1 + 4*x + 18*x^2 + 52*x^3 + 131*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: A121674-A121680.
Sequence in context: A120021 A223897 A131490 * A273997 A051921 A023998
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 15 2006
STATUS
approved

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Last modified April 20 21:11 EDT 2024. Contains 371845 sequences. (Running on oeis4.)