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 A262737 O.g.f. exp( Sum_{n >= 1} A262732(n)*x^n/n ). 5
 1, 8, 95, 1336, 20642, 338640, 5791291, 102108760, 1842857390, 33879118384, 632210693270, 11944142806064, 228010741228740, 4391334026631072, 85221618348230355, 1664901954576830360, 32716286416687895862, 646228961799752926320, 12823701194384778672322 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS O.g.f. is 1/x * the series reversion of x*(1 - x)^k/(1 + x)^(k+2) for k = 3. See the cross references for related sequences obtained from other values of k. LINKS Table of n, a(n) for n=0..18. Peter Bala, Notes on logarithmic differentiation, the binomial transform and series reversion FORMULA a(n-1) = 1/n * Sum_{i = 0..n-1} binomial(5*n,i)*binomial(4*n-i-2,n-i-1). O.g.f.: A(x) = exp ( Sum_{n >= 1} 1/n! * (5*n)!/(5*n/2)! * (3*n/2)!/(3*n)!*x^n/n ) = 1 + 8*x + 195*x^2 + 1336*x^3 + .... 1 + x*A'(x)/A(x) is the o.g.f. for A262732. O.g.f. is the series reversion of x*(1 - x)^3/(1 + x)^5. a(0) = 1 and for n >= 1, a(n) = 1/n * Sum {k = 1..n} 1/k!*(5*k)!/GAMMA(5*k/2+1)*GAMMA(3*k/2+1)/(3*k)! * a(n-k). MAPLE A262737 := proc (n) option remember; if n = 0 then 1 else add(1/k!*(5*k)!/GAMMA(5*k/2 + 1)*GAMMA(3*k/2 + 1)/(3*k)!*A262737(n-k), k = 1 .. n)/n end if; end proc: seq(A262737(n), n = 0 .. 20); PROG (PARI) a(n) = sum(k=0, n, binomial(5*(n+1), k)*binomial(4*(n+1)-k-2, (n+1)-k-1))/(n+1); \\ Altug Alkan, Oct 03 2015 CROSSREFS Cf. A000108 (k = 0), A007297 (k = 1), A066357 (k = 2), A262738 (k = 4), A262739 (k = 5), A262740 (k = 6), A262732. Sequence in context: A099298 A182648 A003775 * A299747 A300261 A121785 Adjacent sequences: A262734 A262735 A262736 * A262738 A262739 A262740 KEYWORD nonn,easy AUTHOR Peter Bala, Sep 29 2015 STATUS approved

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Last modified October 3 18:47 EDT 2023. Contains 365870 sequences. (Running on oeis4.)