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 A144387 Triangle read by rows: row n gives the coefficients in the expansion of Sum_{j=0..n} A000040(j+1)*x^j*(1 - x)^(n - j). 4
 2, 2, 1, 2, -1, 4, 2, -3, 5, 3, 2, -5, 8, -2, 8, 2, -7, 13, -10, 10, 5, 2, -9, 20, -23, 20, -5, 12, 2, -11, 29, -43, 43, -25, 17, 7, 2, -13, 40, -72, 86, -68, 42, -10, 16, 2, -15, 53, -112, 158, -154, 110, -52, 26, 13, 2, -17, 68, -165, 270, -312, 264, -162, 78, -13, 18 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Row sums yield the primes A000040. LINKS G. C. Greubel, Rows n = 0..50 of the triangle, flattened EXAMPLE Triangle begins     2;     2,   1;     2,  -1,  4;     2,  -3,  5,    3;     2,  -5,  8,   -2,   8;     2,  -7, 13,  -10,  10,    5;     2,  -9, 20,  -23,  20,   -5,  12;     2, -11, 29,  -43,  43,  -25,  17,    7;     2, -13, 40,  -72,  86,  -68,  42,  -10, 16;     2, -15, 53, -112, 158, -154, 110,  -52, 26,  13;     2, -17, 68, -165, 270, -312, 264, -162, 78, -13, 18;     ... MATHEMATICA p[x_, n_] = Sum[Prime[k + 1]*x^k*(1 - x)^(n - k), {k, 0, n}]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]//Flatten PROG (Sage) def p(n, x): return sum( nth_prime(j+1)*x^j*(1-x)^(n-j) for j in (0..n) ) def T(n): return ( p(n, x) ).full_simplify().coefficients(sparse=False) [T(n) for n in (0..12)] # G. C. Greubel, Jul 15 2021 CROSSREFS Cf. A122753, A123018, A123019, A123021, A123027, A123199, A123202, A123217, A123221, A141720, A144400, A174128. Sequence in context: A326952 A109909 A254573 * A030768 A051480 A071572 Adjacent sequences:  A144384 A144385 A144386 * A144388 A144389 A144390 KEYWORD sign,tabl AUTHOR Roger L. Bagula and Gary W. Adamson, Oct 01 2008 EXTENSIONS Edited, new name, and offset corrected by Franck Maminirina Ramaharo, Oct 19 2018 STATUS approved

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Last modified November 28 13:47 EST 2021. Contains 349413 sequences. (Running on oeis4.)