A187002 Triangle T(n,m): column m is the expansion of (x+2*x^2+3*x^3+3*x^4+2*x^5+x^6)^m

1, 2, 1, 3, 4, 1, 3, 10, 6, 1, 2, 18, 21, 8, 1, 1, 25, 53, 36, 10, 1, 0, 28, 105, 116, 55, 12, 1, 0, 25, 171, 294, 215, 78, 14, 1, 0, 18, 234, 616, 660, 358, 105, 16, 1, 0, 10, 273, 1098, 1677, 1287, 553, 136, 18, 1, 0, 4, 273, 1696, 3640, 3828, 2275, 808, 171, 20, 1, 0, 1, 234, 2297, 6890, 9739, 7735, 3740, 1131, 210, 22, 1

Offset

1,2

Links

Table of n, a(n) for n=1..78.

Vladimir Kruchinin, Composition of ordinary generating functions, arXiv:1009.2565 [math.CO], 2010.

Formula

T(n,m) := sum(k=m..n, binomial(m,k-m) * sum(j=0..k, binomial(k,j) * binomial(j,n-3*k+2*j))).

Example

1,
2,1,
3,4,1,
3,10,6,1,
2,18,21,8,1,
1,25,53,36,10,1,
0,28,105,116,55,12,1,
0,25,171,294,215,78,14,1

Prog

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

Crossrefs

Sequence in context: A135086 A210561 A210549 * A177226 A059026 A233529

Adjacent sequences: A186999 A187000 A187001 * A187003 A187004 A187005

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Mar 01 2011

Status

approved