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A358091
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Triangle read by rows. Coefficients of the polynomials P(n, x) = 2^(n-2)*(3*n-1)* hypergeometric([-3*n, 1 - n, -n + 4/3], [-n, -n + 1/3], x). T(n, k) = [x^k] P(n, x).
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2
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1, 5, -6, 16, -60, 48, 44, -288, 660, -440, 112, -1056, 4032, -7280, 4368, 272, -3360, 17952, -52224, 81600, -45696, 640, -9792, 67200, -267520, 656640, -930240, 496128, 1472, -26880, 225216, -1133440, 3740352, -8160768, 10767680, -5537664
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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[1] 1;
[2] 5, -6;
[3] 16, -60, 48;
[4] 44, -288, 660, -440;
[5] 112, -1056, 4032, -7280, 4368;
[6] 272, -3360, 17952, -52224, 81600, -45696;
[7] 640, -9792, 67200, -267520, 656640, -930240, 496128;
[8] 1472, -26880, 225216, -1133440, 3740352, -8160768, 10767680, -5537664;
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PROG
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(SageMath)
def P(n):
h = 2^(n-2)*(3*n-1)*hypergeometric([-3*n, 1 - n, -n + 4/3], [-n, -n + 1/3], x)
return h.series(x, n+1).polynomial(SR)
for n in range(1, 9): print(P(n).list())
# To evaluate the polynomials use:
def p(n, t): return Integer(P(n)(x=t).n())
print([p(n, -1/2) for n in range(1, 21)])
print([(-1)^n*p(n + 1, 1) for n in range(0, 22)])
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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