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A276589
Transpose of A276588.
4
1, 3, 2, 11, 8, 6, 49, 38, 30, 24, 261, 212, 174, 144, 120, 1631, 1370, 1158, 984, 840, 720, 11743, 10112, 8742, 7584, 6600, 5760, 5040, 95901, 84158, 74046, 65304, 57720, 51120, 45360, 40320, 876809, 780908, 696750, 622704, 557400, 499680, 448560, 403200, 362880, 8877691, 8000882, 7219974, 6523224, 5900520, 5343120, 4843440, 4394880, 3991680, 3628800
OFFSET
0,2
COMMENTS
Rows give the successive first differences of A001339.
EXAMPLE
The top left corner of the array:
1, 3, 11, 49, 261, 1631, 11743
2, 8, 38, 212, 1370, 10112, 84158
6, 30, 174, 1158, 8742, 74046, 696750
24, 144, 984, 7584, 65304, 622704, 6523224
120, 840, 6600, 57720, 557400, 5900520, 68019240
720, 5760, 51120, 499680, 5343120, 62118720, 780827760
5040, 45360, 448560, 4843440, 56775600, 718709040, 9778048560
MATHEMATICA
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 *)
PROG
(Scheme) (define (A276589 n) (A276588bi (A025581 n) (A002262 n))) ;; Code for A276588bi given in A276588.
(PARI) T(r, c) = sum(k=0, r, binomial(r, k)*(1 + c + k)!);
for(r=0, 10, for(c=0, r, print1(T(r - c, 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(r - c, c) for c in range(r + 1)]) # Indranil Ghosh, Apr 11 2017
CROSSREFS
Topmost row: A001339. For other rows and columns, see the information given in transpose A276588.
Cf. also A276587.
Sequence in context: A191669 A344891 A163841 * A275950 A276587 A180185
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Sep 19 2016
STATUS
approved