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 A180716 G.f.: 1 = Sum_{n>=0} a(n)*x^n * Sum_{k=0..n+1} C(n+1,k)^2*(-x)^k. 4
 1, 1, 4, 35, 524, 11844, 374544, 15740121, 846918340, 56716282700, 4622924730800, 450422314335500, 51679784091622960, 6895215281303487760, 1058342987968671733824, 185145713675921057952219, 36616521252754210909572684, 8128356026325692474893812996 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Compare g.f. to a g.f. of the Catalan numbers (A000108): 1 = Sum_{n>=0} A000108(n)*x^n * Sum_{k=0..n+1} C(n+1,k)*(-x)^k. LINKS EXAMPLE G.f.: 1 = 1*(1-x) + 1*x*(1-2^2*x+x^2) + 4*x^2*(1-3^2*x+3^2*x^2-x^3) + 35*x^3*(1-4^2*x+6^2*x^2-4^2*x^3+x^4) + 524*x^4*(1-5^2*x+10^2*x^2-10^2*x^3+5^2*x^4-x^5) +... PROG (PARI) {a(n)=if(n==0, 1, -polcoeff(sum(m=0, n-1, a(m)*x^m*sum(k=0, m+1, binomial(m+1, k)^2*(-x)^k)+x*O(x^n)), n))} CROSSREFS Cf. A209440. Sequence in context: A287886 A224797 A143669 * A171778 A119391 A177387 Adjacent sequences:  A180713 A180714 A180715 * A180717 A180718 A180719 KEYWORD nonn AUTHOR Paul D. Hanna, Sep 28 2010 STATUS approved

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Last modified November 13 13:15 EST 2018. Contains 317149 sequences. (Running on oeis4.)