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%I #15 Mar 09 2020 12:33:49
%S 1,10,149,2630,51002,1050132,22539085,498732014,11296141454,
%T 260613866380,6103074997890,144696786555580,3466352150674324,
%U 83776927644646952,2040261954214847421,50018542073019175806,1233419779839067305350,30572886836581693309020
%N O.g.f. exp( Sum_{n >= 1} A211419(n)*x^n/n ).
%C 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.
%H Peter Bala, <a href="/A100100/a100100_1.pdf">Notes on logarithmic differentiation, the binomial transform and series reversion</a>
%F a(n-1) = 1/n * Sum_{i = 0..n-1} binomial(6*n,i)*binomial(5*n-i-2,n-i-1).
%F 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 + ....
%F 1 + x*A'(x)/A(x) is the o.g.f. for A211419.
%F O.g.f. is the series reversion of x*(1 - x)^4/(1 + x)^6.
%F 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).
%p 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:
%p seq(A262738(n), n = 0..20);
%o (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
%Y Cf. A211419, A000108 (k = 0), A007297 (k = 1), A066357 (k = 2), A262737 (k = 3), A262739 (k = 5), A262740 (k = 6).
%K nonn,easy
%O 0,2
%A _Peter Bala_, Sep 29 2015
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