A186186 Expansion of 1/(1-x/(1-x)*A(x/(1-x))) where A(x) is the g.f. of A002293.

1, 1, 3, 12, 63, 403, 2919, 22833, 187799, 1599718, 13984383, 124717327, 1130144932, 10375309228, 96290993853, 901915801437, 8514822062757, 80939662475426, 774025387921462, 7441380898249458, 71879194326339456, 697253570563306939, 6789448668631285664, 66340474776507262638

Offset: 0

Author

Vladimir Kruchinin, Feb 14 2011

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..500
• Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

Crossrefs

Cf. A002293.

Programs

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

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.

Extensions

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