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 A080852 Square array of 4D pyramidal numbers, read by antidiagonals. 15
 1, 1, 4, 1, 5, 10, 1, 6, 15, 20, 1, 7, 20, 35, 35, 1, 8, 25, 50, 70, 56, 1, 9, 30, 65, 105, 126, 84, 1, 10, 35, 80, 140, 196, 210, 120, 1, 11, 40, 95, 175, 266, 336, 330, 165, 1, 12, 45, 110, 210, 336, 462, 540, 495, 220, 1, 13, 50, 125, 245, 406, 588, 750, 825, 715, 286, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The first row contains the tetrahedral numbers, which are really three-dimensional, but can be regarded as degenerate 4D pyramidal numbers. - N. J. A. Sloane, Aug 28 2015 LINKS FORMULA T(n, k) = C(k + 3, 3) + n*C(k + 3, 4). T(n, k) = T(n - 1, k) + C(k + 3, 4) = T(n - 1, k) + k(k + 1)(k + 2)(k + 3)/24. G.f. for rows: (1 + nx)/(1 - x)^5, n >= -1. T(n,k) = sum_{j=0..k} A080851(n,j). - R. J. Mathar, Jul 28 2016 EXAMPLE Array, n >= 0, k >= 0, begins 1 4 10 20  35  56 ... 1 5 15 35  70 126 ... 1 6 20 50 105 196 ... 1 7 25 65 140 266 ... 1 8 30 80 175 336 ... PROG (Derive) vector(vector(poly_coeff(Taylor((1+kx)/(1-x)^5, x, 11), x, n), n, 0, 11), k, -1, 10) VECTOR(VECTOR(comb(k+3, 3)+comb(k+3, 4)n, k, 0, 11), n, 0, 11) CROSSREFS Rows include A000292, A000332, A002415, A001296, A002418, A002419, A051740, A051797. Cf. A057145, A080851, A180266. See A257200 for another version of the array. Sequence in context: A155060 A153426 A261720 * A204201 A090842 A120868 Adjacent sequences:  A080849 A080850 A080851 * A080853 A080854 A080855 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Feb 21 2003 STATUS approved

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Last modified April 21 02:10 EDT 2021. Contains 343143 sequences. (Running on oeis4.)