A202550 Triangle T(n,m) = coefficient of x^n in the Taylor expansion of [(1-(1-8*x)^(1/4))/(1+(1-8*x)^(1/4))]^m.

1, 4, 1, 21, 8, 1, 124, 58, 12, 1, 782, 416, 111, 16, 1, 5144, 2997, 940, 180, 20, 1, 34845, 21752, 7653, 1760, 265, 24, 1, 241196, 159062, 61068, 16014, 2940, 366, 28, 1, 1697498, 1171136, 481944, 139712, 29600, 4544

Offset

1,2

Links

Table of n, a(n) for n=1..42.

Formula

n*T(n,m) = sum_{i=m..n} i*binomial(i-1,m-1)* sum_{k=0..n-i} (-1)^(n-k-i)*binomial(n+k-1,n-1) *sum_{j=0..k} binomial(j,n-3*k+2*j-i)*binomial(k,j) *2^(2*n-5*k+3*j-2*i) *3^(-n+3*k-j+i).

Example

The coefficients start in row n=1 with 1<=m<=n as:
1,
4, 1,
21, 8, 1,
124, 58, 12, 1,
782, 416, 111, 16, 1,
5144, 2997, 940, 180, 20, 1,
34845, 21752, 7653, 1760, 265, 24, 1

Maple

A202550 := proc(n, m)
        (1-(1-8*x)^(1/4)) /(1+(1-8*x)^(1/4)) ;
        coeftayl(%^m, x=0, n) ;
end proc: # R. J. Mathar, Dec 22 2011

Prog

(Maxima) T(n, m):=sum(i*binomial(i-1, m-1)*sum((-1)^(n-k-i)*binomial(n+k-1, n-1)*sum(binomial(j, n-3*k+2*j-i)*binomial(k, j)*2^(2*n-5*k+3*j-2*i)*3^(-n+3*k-j+i), j, 0, k), k, 0, n-i), i, m, n)/n;

Crossrefs

Cf. A101478.

Sequence in context: A121336 A126457 A159841 * A364760 A142472 A360089

Adjacent sequences: A202547 A202548 A202549 * A202551 A202552 A202553

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Dec 20 2011

Status

approved