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A276589 Transpose of A276588.

%I A276589 #25 Sep 24 2024 14:42:22
%S A276589 1,3,2,11,8,6,49,38,30,24,261,212,174,144,120,1631,1370,1158,984,840,
%T A276589 720,11743,10112,8742,7584,6600,5760,5040,95901,84158,74046,65304,
%U A276589 57720,51120,45360,40320,876809,780908,696750,622704,557400,499680,448560,403200,362880,8877691,8000882,7219974,6523224,5900520,5343120,4843440,4394880,3991680,3628800
%N A276589 Transpose of A276588.
%C A276589 Rows give the successive first differences of A001339.
%H A276589 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%e A276589 The top left corner of the array:
%e A276589      1,     3,     11,      49,      261,      1631,      11743
%e A276589      2,     8,     38,     212,     1370,     10112,      84158
%e A276589      6,    30,    174,    1158,     8742,     74046,     696750
%e A276589     24,   144,    984,    7584,    65304,    622704,    6523224
%e A276589    120,   840,   6600,   57720,   557400,   5900520,   68019240
%e A276589    720,  5760,  51120,  499680,  5343120,  62118720,  780827760
%e A276589   5040, 45360, 448560, 4843440, 56775600, 718709040, 9778048560
%t A276589 T[r_, c_]:=Sum[Binomial[r, k](1 + c + k)!, {k, 0, r}]; Table[T[r - c, c], {r, 0, 10}, {c, 0, r}] // Flatten (* _Indranil Ghosh_, Apr 11 2017 *)
%o A276589 (Scheme) (define (A276589 n) (A276588bi (A025581 n) (A002262 n))) ;; Code for A276588bi given in A276588.
%o A276589 (PARI) T(r, c) = sum(k=0, r, binomial(r, k)*(1 + c + k)!);
%o A276589 for(r=0, 10, for(c=0, r, print1(T(r - c, c),", ");); print();) \\ _Indranil Ghosh_, Apr 11 2017
%o A276589 (Python)
%o A276589 from sympy import binomial, factorial
%o A276589 def T(r, c): return sum([binomial(r, k) * factorial(1 + c + k) for k in range(r + 1)])
%o A276589 for r in range(11): print([T(r - c, c) for c in range(r + 1)]) # _Indranil Ghosh_, Apr 11 2017
%Y A276589 Topmost row: A001339. For other rows and columns, see the information given in transpose A276588.
%Y A276589 Cf. also A276587.
%K A276589 nonn,tabl
%O A276589 0,2
%A A276589 _Antti Karttunen_, Sep 19 2016