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A186186 Expansion of 1/(1-x/(1-x)*A(x/(1-x))) where A(x) is the g.f. of A002293. 1
1, 1, 3, 12, 63, 403, 2919, 22833, 187799, 1599718, 13984383, 124717327, 1130144932, 10375309228, 96290993853, 901915801437, 8514822062757, 80939662475426, 774025387921462, 7441380898249458, 71879194326339456, 697253570563306939, 6789448668631285664, 66340474776507262638 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..500

Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582.

FORMULA

a(n) = Sum_{m=1..n} Sum_{k=m..n} binomial(n-1,k-1)*m/(3*k-2*m)*binomial(4*k-3*m-1,k-m), n>0, a(0)=1.

PROG

(PARI) a(n)={if(n<1, n==0, sum(m=1, n, sum(k=m, n, binomial(n-1, k-1)*m/(3*k-2*m)*binomial(4*k-3*m-1, k-m))))} \\ Andrew Howroyd, Apr 17 2021

CROSSREFS

Cf. A002293.

Sequence in context: A307708 A308206 A264151 * A238887 A135889 A124562

Adjacent sequences:  A186183 A186184 A186185 * A186187 A186188 A186189

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, Feb 14 2011

EXTENSIONS

Terms a(18) and beyond from Andrew Howroyd, Apr 17 2021

STATUS

approved

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Last modified June 19 03:23 EDT 2021. Contains 345125 sequences. (Running on oeis4.)