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A185655
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a(n) = Sum_{k=0..n} C(n+k, k)*C(n+k+1, k+1)/(n+1).
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0
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1, 4, 27, 236, 2375, 26090, 304241, 3704860, 46622655, 602035556, 7937288062, 106451074614, 1448267147717, 19944962832826, 277565209168861, 3898075200816892, 55182857681572655, 786731161113510584
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OFFSET
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0,2
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COMMENTS
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The function B(x,r) = x*Sum_{n>=0} b(n,r)*x^n, where
b(n,r) = Sum_{k=0..n} C(n+k, k)*C(n+k+1, r*k+1)/(n+1), satisfies
B(x/(1+x) - x^r, r) = x for all positive integer r except at r=1;
B(x,1)/x is the generating function of this sequence.
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LINKS
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Table of n, a(n) for n=0..17.
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EXAMPLE
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G.f.: A(x) = 1 + 4*x + 27*x^2 + 236*x^3 + 2375*x^4 + 26090*x^5 +...
Let G(x*A(x)) = x, then the series reversion of x*A(x) begins:
G(x) = x - 4*x^2 + 5*x^3 - 16*x^4 - 12*x^5 - 218*x^6 - 1197*x^7 - 8974*x^8 - 65582*x^9 - 503614*x^10 - 3956461*x^11 -...
Does G(x) satisfy a nice functional equation?
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PROG
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(PARI) {a(n)=sum(k=0, n, binomial(n+k, k)*binomial(n+k+1, k+1))/(n+1)}
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CROSSREFS
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Sequence in context: A059391 A190738 A160883 * A181146 A161120 A183430
Adjacent sequences: A185647 A185653 A185654 * A185656 A185657 A185658
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Feb 15 2011
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STATUS
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approved
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