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 A276588 Square array A(row,col) = Sum_{k=0..row} binomial(row,k)*(1+col+k)!, read by descending antidiagonals as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ... 8
 1, 2, 3, 6, 8, 11, 24, 30, 38, 49, 120, 144, 174, 212, 261, 720, 840, 984, 1158, 1370, 1631, 5040, 5760, 6600, 7584, 8742, 10112, 11743, 40320, 45360, 51120, 57720, 65304, 74046, 84158, 95901, 362880, 403200, 448560, 499680, 557400, 622704, 696750, 780908, 876809, 3628800, 3991680, 4394880, 4843440, 5343120, 5900520, 6523224, 7219974, 8000882, 8877691 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA A(row,col) = Sum_{k=0..row} binomial(row,k)*A000142(1+col+k). A(row,col) = A276075(A066117(row+1,col+1)). EXAMPLE The top left corner of the array:      1,     2,     6,     24,     120,      720,      5040,      40320      3,     8,    30,    144,     840,     5760,     45360,     403200     11,    38,   174,    984,    6600,    51120,    448560,    4394880     49,   212,  1158,   7584,   57720,   499680,   4843440,   51932160    261,  1370,  8742,  65304,  557400,  5343120,  56775600,  661933440   1631, 10112, 74046, 622704, 5900520, 62118720, 718709040, 9059339520 MATHEMATICA T[r_, c_]:=Sum[Binomial[r, k](1 + c + k)!, {k, 0, r}]; Table[T[c, r - c], {r, 0, 10}, {c, 0, r}] // Flatten (* Indranil Ghosh, Apr 11 2017 *) PROG (Scheme) (define (A276588 n) (A276588bi (A002262 n) (A025581 n))) (define (A276588bi row col) (A276075 (A066117bi (+ 1 row) (+ 1 col)))) ;; Code for A066117bi given in A066117, and for A276075 under the respective entry. (PARI) T(r, c) = sum(k=0, r, binomial(r, k)*(1 + c + k)!); for(r=0, 10, for(c=0, r, print1(T(c, r - c), ", "); ); print(); ) \\ Indranil Ghosh, Apr 11 2017 (Python) from sympy import binomial, factorial def T(r, c): return sum([binomial(r, k) * factorial(1 + c + k) for k in range(r + 1)]) for r in range(11): print [T(c, r - c) for c in range(r + 1)] # Indranil Ghosh, Apr 11 2017 CROSSREFS Transpose: A276589. Topmost row (row 0): A000142, Row 1: A001048 (without its initial 2), Row 2: A001344 (from a(1) = 11 onward), Row 3: A001345 (from a(1) = 49 onward), Row 4: A001346 (from a(1) = 261 onward), Row 5: A001347 (from a(1) = 1631 onward). Leftmost column (column 0): A001339, Column 1: A001340, Columns 2-3: A001341 & A001342 (apparently). Cf. A276075. Cf. also arrays A066117, A276586, A099884, A255483. Sequence in context: A242340 A033766 A129340 * A275951 A276586 A080598 Adjacent sequences:  A276585 A276586 A276587 * A276589 A276590 A276591 KEYWORD nonn,tabl AUTHOR Antti Karttunen, Sep 19 2016 STATUS approved

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Last modified June 5 18:48 EDT 2020. Contains 334854 sequences. (Running on oeis4.)