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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
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 (list; table; graph; refs; listen; history; text; internal format)
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 * A153920 A300483 A294241

Adjacent sequences:  A338369 A338370 A338371 * A338373 A338374 A338375

KEYWORD

nonn,tabl

AUTHOR

Vladimir Kruchinin, Oct 23 2020

STATUS

approved

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Last modified June 16 04:44 EDT 2021. Contains 345056 sequences. (Running on oeis4.)