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EXAMPLE
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Triangle begins:
[1],
[14, 8, 2],
[786, 1056, 576, 96, 6],
[61340, 131760, 117900, 48320, 9540, 720, 20],
[5562130, 16481920, 20917120, 13847680, 5118400, 1025920, 105280, 4480, 70],
[549676764, 2079579600, 3444581700, 3165926400, 1755532800, 598123008, 123656400, 14716800, 926100, 25200, 252],
[57440496036, 264565490112, 542687590368, 640299696960, 477284304420, 233110386432, 75243589344, 15835792896, 2103157980, 165802560, 7051968, 133056, 924],
[6242164112184, 33895475918304, 83073660613944, 119912994225024, 112698387745944, 72172565713248, 32111980788888, 9951304416768, 2124873478728, 305035899168, 28270554312, 1584815232, 48600552, 672672, 3432],
[698300344311570, 4368053451041280, 12465205610457600, 21305587665922560, 24216302627637120, 19255941998092800, 10989839486545920, 4550117424652800, 1366687981264320, 295074717949440, 44954858108160, 4691645038080, 320878958400, 13445752320, 311351040, 3294720, 12870], ...
where this triangle forms the coefficients in the series
B(x,y) = 1/(1-x-x*y) +
(14 + 8*(x+x*y) + 2*(x+x*y)^2) * x^2*y/(1-x-x*y)^5 +
(786 + 1056*(x+x*y) + 576*(x+x*y)^2 + 96*(x+x*y)^3 + 6*(x+x*y)^4) * x^4*y^2/(1-x-x*y)^9 +
(61340 + 131760*(x+x*y) + 117900*(x+x*y)^2 + 48320*(x+x*y)^3 + 9540*(x+x*y)^4 + 720*(x+x*y)^5 + 20*(x+x*y)^6) * x^6*y^3/(1-x-x*y)^13 +...
such that the sum may be expressed using binomial coefficients C(n,k)^4 like so:
B(x,y) = 1 +
x*(1 + y) +
x^2*(1 + 2^4*y + y^2) +
x^3*(1 + 3^4*y + 3^4*y^2 + y^3) +
x^4*(1 + 4^4*y + 6^4*y^2 + 4^4*y^3 + y^4) +
x^5*(1 + 5^4*y + 10^4*y^2 + 10^4*y^3 + 5^4*y^4 + y^5) +
x^6*(1 + 6^4*y + 15^4*y^2 + 20^4*y^3 + 15^4*y^4 + 6^4*y^5 + y^6) +...
The central terms of the rows begin:
[1, 8, 576, 48320, 5118400, 598123008, 75243589344, 9951304416768, 1366687981264320, ...].
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