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 A227076 A triangle formed like Pascal's triangle, but with 5^n on the borders instead of 1. 5
 1, 5, 5, 25, 10, 25, 125, 35, 35, 125, 625, 160, 70, 160, 625, 3125, 785, 230, 230, 785, 3125, 15625, 3910, 1015, 460, 1015, 3910, 15625, 78125, 19535, 4925, 1475, 1475, 4925, 19535, 78125, 390625, 97660, 24460, 6400, 2950, 6400, 24460, 97660, 390625 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS All rows except the zeroth are divisible by 5. Is there a closed-form formula for these numbers, like for binomial coefficients? LINKS T. D. Noe, Rows n = 0..50 of triangle, flattened FORMULA T(n,0) = 5^n. T(n,1) = 5*A047850(n-1). T(n,2) = 5*(5^n/80 + 3*n/4 + 51/16). T(n,3) = 5*(5^n/320 + 45*n/16 + 3*n^2/8 + 819/64). - R. J. Mathar, Aug 09 2013 EXAMPLE Example: 1, 5, 5, 25, 10, 25, 125, 35, 35, 125, 625, 160, 70, 160, 625, 3125, 785, 230, 230, 785, 3125, 15625, 3910, 1015, 460, 1015, 3910, 15625, 78125, 19535, 4925, 1475, 1475, 4925, 19535, 78125, 390625, 97660, 24460, 6400, 2950, 6400, 24460, 97660, 390625 MAPLE A227076 := proc(n, k)     if k = 0 or k = n then         5^n ;     elif k < 0 or k > n then         0;     else         procname(n-1, k)+procname(n-1, k-1) ;     end if; end proc: # R. J. Mathar, Aug 09 2013 MATHEMATICA t = {}; Do[r = {}; Do[If[k == 0 || k == n, m = 5^n, m = t[[n, k]] + t[[n, k + 1]]]; r = AppendTo[r, m], {k, 0, n}]; AppendTo[t, r], {n, 0, 10}]; t = Flatten[t] CROSSREFS Cf. A007318 (Pascal's triangle), A228053 ((-1)^n on the borders). Cf. A051601 (n on the borders), A137688 (2^n on borders). Cf. A083585 (row sums: (8*5^n - 5*2^n)/3), A227074 (4^n edges), A227075 (3^n edges). Sequence in context: A256693 A255458 A256135 * A223186 A071340 A056451 Adjacent sequences:  A227073 A227074 A227075 * A227077 A227078 A227079 KEYWORD nonn,tabl AUTHOR T. D. Noe, Aug 06 2013 STATUS approved

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Last modified August 13 07:13 EDT 2022. Contains 356078 sequences. (Running on oeis4.)