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

0,3

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.

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 * A355164 A373770 A381210

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