A188110 Triangle T(n,m), [x*A(x)]^m=sum(n>=m T(n,m)*x^n), where A(x) satisfies x*A(x)^3= -(2*x*A(x)^2+sqrt(1-4*x*A(x)^2)-1)/(4*x*A(x)^2+sqrt(1-4*x*A(x)^2)-1)

1, 3, 1, 28, 6, 1, 350, 65, 9, 1, 5020, 868, 111, 12, 1, 78023, 12924, 1581, 166, 15, 1, 1278340, 205766, 24468, 2516, 230, 18, 1, 21740636, 3428438, 399735, 40489, 3700, 303, 21, 1, 380161308, 59034600, 6784186, 679460, 61905, 5160, 385, 24, 1, 6792111260, 1042169972, 118444293, 11759612, 1067738, 89715, 6923, 476, 27, 1

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

Formula

T(n,m) = m/(2*n-m)*A035324(3*n-2*m,2*n-m).

Mathematica

(* S = A035324 *)
S[n_, m_] /; n >= m >= 1 := S[n, m] = 2(2(n-1) + m)(S[n - 1, m]/n) + m (S[n - 1, m - 1]/n); S[n_, m_] /; n < m = 0; S[n_, 0] = 0; S[1, 1] = 1;
T[n_, m_] := m/(2n-m) S[3n - 2m, 2n - m];
Table[T[n, m], {n, 1, 10}, {m, 1, n}] // Flatten (* Jean-François Alcover, Feb 16 2019 *)

Crossrefs

Cf. A035324.

Sequence in context: A165624 A287206 A288517 * A358165 A298399 A365087

Adjacent sequences: A188107 A188108 A188109 * A188111 A188112 A188113

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Mar 21 2011

Status

approved