A177970 Array T(n,m) = A177944(2*n,2*m) read by antidiagonals.
1, 1, 1, 1, 26, 1, 1, 99, 99, 1, 1, 244, 622, 244, 1, 1, 485, 2300, 2300, 485, 1, 1, 846, 6423, 12000, 6423, 846, 1, 1, 1351, 15001, 45031, 45031, 15001, 1351, 1, 1, 2024, 30924, 136120, 218774, 136120, 30924, 2024, 1, 1, 2889, 58122, 352698, 831384
Offset: 0
Examples
The table starts in row n=0, column m=0 as: 1, 1, 1, 1, 1, 1, 1, 1, 1, 26, 99, 244, 485, 846, 1351, 2024, 1, 99, 622, 2300, 6423, 15001, 30924, 58122, 1, 244, 2300, 12000, 45031, 136120, 352698, 813940, 1, 485, 6423, 45031, 218774, 831384, 2645350, 7354688, 1, 846, 15001, 136120, 831384, 3879856, 14872836, 49031376, 1, 1351, 30924, 352698, 2645350, 14872836, 67603876, 260757874, 1, 2024, 58122, 813940, 7354688, 49031376, 260757874,1163381372,
Links
- Robert Israel, Table of n, a(n) for n = 0..10000
Programs
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Maple
T:= (m,n) -> (2*n+1)*binomial(2*m+1+2*n, 2*m)-2*n-2*m: seq(seq(T(m,s-m),m=0..s),s=0..10); # Robert Israel, Jul 06 2017
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Mathematica
t[n_, m_] = 1/Beta[2*n + 1, 2*m + 1] - 2*n - 2*m; a = Table[Table[t[n, m], {m, 0, 10}], {n, 0, 10}]; Table[Table[a[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}]; Flatten[%] -
Python
from sympy import binomial def T(m, n): return (2*n + 1)*binomial(2*m + 1 + 2*n, 2*m) - 2*n - 2*m for n in range(11): print([T(m, n - m) for m in range(n + 1)]) # Indranil Ghosh, Jul 06 2017
Formula
T(n,m) = 1/Beta(2*n+1, 2*m+1) - 2*n - 2*m where Beta(a,b) = Gamma(a)*Gamma(b)/Gamma(a+b).
Extensions
Definition rewritten with A177944, examples brought into normal form, closed sum formula - The Assoc. Eds. of the OEIS, Nov 03 2010
Comments