A276589 Transpose of A276588.

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

Author

Antti Karttunen, Sep 19 2016

Keywords

• nonn
• tabl

Comments

Rows give the successive first differences of A001339.

Examples

			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
		

Links

• Index entries for sequences related to factorial base representation

Crossrefs

Topmost row: A001339. For other rows and columns, see the information given in transpose A276588.

Cf. also A276587.

Programs

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 *)

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

Scheme

(define (A276589 n) (A276588bi (A025581 n) (A002262 n))) ;; Code for A276588bi given in A276588.