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A262738
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O.g.f. exp( Sum_{n >= 1} A211419(n)*x^n/n ).
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5
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1, 10, 149, 2630, 51002, 1050132, 22539085, 498732014, 11296141454, 260613866380, 6103074997890, 144696786555580, 3466352150674324, 83776927644646952, 2040261954214847421, 50018542073019175806, 1233419779839067305350, 30572886836581693309020
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OFFSET
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0,2
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COMMENTS
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O.g.f. is 1/x * the series reversion of x*(1 - x)^k/(1 + x)^(k+2) at k = 4. See the cross references for related sequences obtained from other values of k.
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LINKS
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FORMULA
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a(n-1) = 1/n * Sum_{i = 0..n-1} binomial(6*n,i)*binomial(5*n-i-2,n-i-1).
O.g.f.: A(x) = exp ( Sum_{n >= 1} (6*n)!*(2*n)!/((4*n)!*(3*n)!*n!)*x^n/n ) = 1 + 10*x + 149*x^2 + 2630*x^3 + ....
1 + x*A'(x)/A(x) is the o.g.f. for A211419.
O.g.f. is the series reversion of x*(1 - x)^4/(1 + x)^6.
a(0) = 1 and for n >= 1, a(n) = 1/n * Sum {k = 1..n} (6*k)!*(2*k)!/((4*k)!*(3*k)!*k!)*a(n-k).
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MAPLE
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A262738 := proc(n) option remember; if n = 0 then 1 else add((6*k)!*(2*k)!/((4*k)!*(3*k)!*k!)*A262738(n-k), k = 1 .. n)/n end if; end proc:
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PROG
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(PARI) a(n) = sum(k=0, n, binomial(6*(n+1), k)*binomial(5*(n+1)-k-2, (n+1)-k-1))/(n+1); \\ Altug Alkan, Oct 03 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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