A338372 T(n, m) = Sum_{k=1..(m+3)/2} C(m-k+2, k-1)*C(n+1, k-1)*C(n-m+k-1, k-1)*C(2*n-2*k+4, 2*m-4*k+5)/(C(2*k-2, k-1)*C(2*m-2*k+4, 2*k-2))/2, triangle read by rows.

1, 2, 2, 3, 10, 4, 4, 28, 32, 8, 5, 60, 136, 88, 16, 6, 110, 416, 504, 224, 32, 7, 182, 1036, 2024, 1616, 544, 64, 8, 280, 2240, 6448, 8064, 4736, 1280, 128, 9, 408, 4368, 17424, 31456, 28288, 13056, 2944, 256, 10, 570, 7872, 41616, 102592, 130880, 90880, 34432, 6656, 512, 11, 770, 13332, 90288, 291808, 501568, 487040, 273792, 87808, 14848, 1024

Offset

0,2

Links

Table of n, a(n) for n=0..65.

Formula

G.f.: -1/(x^2*y^2 - (1 - x*(y + 2*A001263(x, y) + 1))^2) = 1/(1 - 2*x^2*y + x^2 - 2*x*y - 2*x).

Example

1,
2, 2,
3, 10, 4,
4, 28, 32, 8,
5, 60, 136, 88, 16

Maple

ogf := 1/(1 -2*x^2*y + x^2 - 2*x*y - 2*x): ser := series(ogf, x, 22):
xser := n -> expand(coeff(ser, x, n)):
seq(seq(coeff(xser(n), y, k), k=0..n), n=0..10); # Peter Luschny, Oct 23 2020

Prog

(Maxima)
T(n, m):=sum((binomial(m-k+2, k-1)*binomial(n+1, k-1)*binomial(n-m+k-1, k-1)*binomial(2*n-2*k+4, 2*m-4*k+5))/(binomial(2*k-2, k-1)*binomial(2*m-2*k+4, 2*k-2)), k, 1, (m+3)/2)/2;

Crossrefs

Cf. A001263, A008459

Sequence in context: A091044 A079661 A220644 * A376723 A153920 A300483

Adjacent sequences: A338369 A338370 A338371 * A338373 A338374 A338375

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Oct 23 2020

Status

approved