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A121679
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a(n) = A121678(n)/(n+1) = [x^n] (1 + x*(1+x)^n )^(n+1) / (n+1).
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3
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1, 1, 3, 13, 85, 706, 7042, 81887, 1081257, 15911488, 257476901, 4533396418, 86110501919, 1752312402881, 37982176570353, 872648321081531, 21162807249523025, 539772371783003416, 14433746294326451095
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n) = Sum_{k=0..n+1} C(n+1,k) * C(n*k,n-k) / (n+1).
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EXAMPLE
| At n=5, a(5) = [x^5] (1 + x*(1+x)^5)^6/6 = 4236/6 = 706, since
(1+x*(1+x)^5)^6 = 1 + 6*x + 45*x^2 + 230*x^3 + 1050*x^4 + 4236*x^5 +...
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PROG
| (PARI) a(n)=sum(k=0, n+1, binomial(n+1, k)*binomial(n*k, n-k))/(n+1)
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CROSSREFS
| Cf. A121678; variants: A121673-A121676, A121680.
Sequence in context: A152789 A192943 A125500 * A023037 A157451 A152112
Adjacent sequences: A121676 A121677 A121678 * A121680 A121681 A121682
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 15 2006
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