A254322 -id:A254322 - cp's OEIS frontend

A256890 Triangle T(n,k) = t(n-k, k); t(n,m) = f(m)t(n-1,m) + f(n)t(n,m-1), where f(x) = x + 2.

1, 2, 2, 4, 12, 4, 8, 52, 52, 8, 16, 196, 416, 196, 16, 32, 684, 2644, 2644, 684, 32, 64, 2276, 14680, 26440, 14680, 2276, 64, 128, 7340, 74652, 220280, 220280, 74652, 7340, 128, 256, 23172, 357328, 1623964, 2643360, 1623964, 357328, 23172, 256, 512, 72076, 1637860, 10978444, 27227908, 27227908, 10978444, 1637860, 72076, 512

Offset: 0

Dale Gerdemann, Apr 12 2015

Related triangles may be found by varying the function f(x). If f(x) is a linear function, it can be parameterized as f(x) = a*x + b. With different values for a and b, the following triangles are obtained:
  a\b 1.......2.......3.......4.......5.......6
  -1  A144431
  0   A007318 A038208 A038221
  1   A008292 A256890 A257180 A257606 A257607
  2   A060187 A257609 A257611 A257613 A257615
  3   A142458 A257610 A257620 A257622 A257624 A257626
  4   A142459 A257612 A257621
  5   A142460 A257614 A257623
  6   A142461 A257616 A257625
  7   A142462 A257617 A257627
  8   A167884 A257618
  9   A257608 A257619
The row sums of these, and similarly constructed number triangles, are shown in the following table:
  a\b 1.......2.......3.......4.......5.......6.......7.......8.......9
  0   A000079 A000302 A000400
  1   A000142 A001715 A001725 A049388 A049198
  2   A000165 A002866 A002866 A051580 A051582
  3   A008544 A051578 A037559 A051605 A051607 A051609
  4   A001813 A047053 A000407 A034177 A051618 A051620 A051622
  5   A047055 A008546 A008548 A034300 A034325 A051688 A051690
  6   A047657 A049308 A047058 A034689 A034724 A034788 A053101 A053103
  7   A084947 A144827 A049209 A045754 A034830 A034832 A034834 A053105
  8   A084948 A144828 A147626 A051189 A034908 A034910 A034912 A034976 A053115
  9   A084949 A144829 A147630 A049211 A045756 A035013 A035018 A035021 A035023
  10                                  A051262 A035265 A035273         A035277
  11                                  A254322
  12                                          A145448
The formula can be further generalized to: t(n,m) = f(m+s)*t(n-1,m) + f(n-s)*t(n,m-1), where f(x) = a*x + b. The following table specifies triangles with nonzero values for s (given after the slash).
  a\b  0           1           2          3
  -2   A130595/1
  -1
  0
  1    A110555/-1  A120434/-1  A144697/1  A144699/2
With the absolute value, f(x) = |x|, one obtains A038221/3, A038234/4, A038247/5, A038260/6, A038273/7, A038286/8, A038299/9 (with value for s after the slash).
If f(x) = A000045(x) (Fibonacci) and s = 1, the result is A010048 (Fibonomial).
In the notation of Carlitz and Scoville, this is the triangle of generalized Eulerian numbers A(r, s | alpha, beta) with alpha = beta = 2. Also the array A(2,1,4) in the notation of Hwang et al. (see page 31). - Peter Bala, Dec 27 2019

			Array, t(n, k), begins as:
   1,    2,      4,        8,        16,         32,          64, ...;
   2,   12,     52,      196,       684,       2276,        7340, ...;
   4,   52,    416,     2644,     14680,      74652,      357328, ...;
   8,  196,   2644,    26440,    220280,    1623964,    10978444, ...;
  16,  684,  14680,   220280,   2643360,   27227908,   251195000, ...;
  32, 2276,  74652,  1623964,  27227908,  381190712,  4677894984, ...;
  64, 7340, 357328, 10978444, 251195000, 4677894984, 74846319744, ...;
Triangle, T(n, k), begins as:
    1;
    2,     2;
    4,    12,      4;
    8,    52,     52,       8;
   16,   196,    416,     196,      16;
   32,   684,   2644,    2644,     684,      32;
   64,  2276,  14680,   26440,   14680,    2276,     64;
  128,  7340,  74652,  220280,  220280,   74652,   7340,   128;
  256, 23172, 357328, 1623964, 2643360, 1623964, 357328, 23172,   256;

Michael De Vlieger, Table of n, a(n) for n = 0..11475 (rows 0 <= n <= 150, flattened.)
L. Carlitz and R. Scoville, Generalized Eulerian numbers: combinatorial applications, J. für die reine und angewandte Mathematik, 265 (1974): 110-37. See Section 3.
Dale Gerdemann, A256890, Plot of t(m,n) mod k , YouTube, 2015.
Hsien-Kuei Hwang, Hua-Huai Chern, and Guan-Huei Duh, An asymptotic distribution theory for Eulerian recurrences with applications, arXiv:1807.01412 [math.CO], 2018-2019.

Cf. A000079, A001715, A008292, A038208, A257180, A257606, A257607, A257609.

Cf. A257610, A257612, A257614, A257616, A257617, A257618, A257619.

A256890:= func< n,k | (&+[(-1)^(k-j)*Binomial(j+3,j)*Binomial(n+4,k-j)*(j+2)^n: j in [0..k]]) >;
[A256890(n,k): k in [0..n], n in [0..10]]; // G. C. Greubel, Oct 18 2022

Table[Sum[(-1)^(k-j)*Binomial[j+3, j] Binomial[n+4, k-j] (j+2)^n, {j,0,k}], {n,0, 9}, {k,0,n}]//Flatten (* Michael De Vlieger, Dec 27 2019 *)

t(n,m) = if ((n<0) || (m<0), 0, if ((n==0) && (m==0), 1, (m+2)*t(n-1, m) + (n+2)*t(n, m-1)));
tabl(nn) = {for (n=0, nn, for (k=0, n, print1(t(n-k, k), ", ");); print(););} \\ Michel Marcus, Apr 14 2015

def A256890(n,k): return sum((-1)^(k-j)*Binomial(j+3,j)*Binomial(n+4,k-j)*(j+2)^n for j in range(k+1))
flatten([[A256890(n,k) for k in range(n+1)] for n in range(11)]) # G. C. Greubel, Oct 18 2022

T(n,k) = t(n-k, k); t(0,0) = 1, t(n,m) = 0 if n < 0 or m < 0 else t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), where f(x) = x + 2.
Sum_{k=0..n} T(n, k) = A001715(n).
T(n,k) = Sum_{j = 0..k} (-1)^(k-j)*binomial(j+3,j)*binomial(n+4,k-j)*(j+2)^n. - Peter Bala, Dec 27 2019
Modified rule of Pascal: T(0,0) = 1, T(n,k) = 0 if k < 0 or k > n else T(n,k) = f(n-k) * T(n-1,k-1) + f(k) * T(n-1,k), where f(x) = x + 2. - Georg Fischer, Nov 11 2021
From G. C. Greubel, Oct 18 2022: (Start)
T(n, n-k) = T(n, k).
T(n, 0) = A000079(n). (End)

A049209 a(n) = -Product_{k=0..n} (7*k-1); sept-factorial numbers.

Original entry on oeis.org

1, 6, 78, 1560, 42120, 1432080, 58715280, 2818333440, 155008339200, 9610517030400, 663125675097600, 50397551307417600, 4182996758515660800, 376469708266409472000, 36517561701841718784000, 3797826416991538753536000, 421558732286060801642496000

Offset: 0

Wolfdieter Lang

G. C. Greubel, Table of n, a(n) for n = 0..330
Index entries for sequences related to factorial numbers.

Cf. A034833, A045754, A048994, A051188, A084947, A144739, A144827, A147585.
Row sums of triangle A051186 (scaled Stirling1 triangle).
Sequences of the form m^n*Pochhammer((m-1)/m, n): A000007 (m=1), A001147 (m=2), A008544 (m=3), A008545 (m=4), A008546 (m=5), A008543 (m=6), this sequence (m=7), A049210 (m=8), A049211 (m=9), A049212 (m=10), A254322 (m=11), A346896 (m=12).

[ -&*[ (7*k-1): k in [0..n-1] ]: n in [1..15] ]; // Klaus Brockhaus, Nov 10 2008

CoefficientList[Series[(1-7*x)^(-6/7),{x,0,20}],x] * Range[0,20]! (* Vaclav Kotesovec, Jan 28 2015 *)
With[{m=7}, Table[m^n*Pochhammer[(m-1)/m, n], {n, 0, 30}]] (* G. C. Greubel, Feb 16 2022 *)

m=7; [m^n*rising_factorial((m-1)/m, n) for n in (0..30)] # G. C. Greubel, Feb 16 2022

a(n) = 6*A034833(n) = (7*n-1)*(!^7), n >= 1, a(0) := 1.
a(n) = Product_{k=1..n} (7*k - 1). a(0) = 1; a(n) = (7*n - 1)*a(n-1) for n > 0. - Klaus Brockhaus, Nov 10 2008
G.f.: 1/(1-6*x/(1-7*x/(1-13*x/(1-14*x/(1-20*x/(1-21*x/(1-27*x/(1-28*x/(1-...(continued fraction). - Philippe Deléham, Jan 08 2012
a(n) = (-1)^n*Sum_{k=0..n} 7^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. - Mircea Merca, May 03 2012
a(n) = 7^n * Gamma(n+6/7) / Gamma(6/7). - Vaclav Kotesovec, Jan 28 2015
E.g.f.: (1-7*x)^(-6/7). - Vaclav Kotesovec, Jan 28 2015
From Nikolaos Pantelidis, Dec 19 2020: (Start)
G.f.: 1/G(0) where G(k) = 1 - (14*k+6)*x - 7*(k+1)*(7*k+6)*x^2/G(k+1); (continued fraction).
which starts as 1/(1-6*x-42*x^2/(1-20*x-182*x^2/(1-34*x-420*x^2/(1-48*x-756*x^2/(1-62*x-1190*x^2/(1-... )))))) (Jacobi continued fraction).
G.f.: 1/Q(0) where Q(k) = 1 - (7*k+6)*x/(1 - (7*k+7)*x/Q(k+1) ); (continued fraction). (End)
Sum_{n>=0} 1/a(n) = 1 + (e/7)^(1/7)*(Gamma(6/7) - Gamma(6/7, 1/7)). - Amiram Eldar, Dec 19 2022

A017509 a(n) = 11*n + 10.

Original entry on oeis.org

10, 21, 32, 43, 54, 65, 76, 87, 98, 109, 120, 131, 142, 153, 164, 175, 186, 197, 208, 219, 230, 241, 252, 263, 274, 285, 296, 307, 318, 329, 340, 351, 362, 373, 384, 395, 406, 417, 428, 439, 450, 461, 472, 483, 494, 505, 516, 527, 538, 549, 560, 571, 582

Offset: 0

N. J. A. Sloane

If k is any member of A045572, the sequence lists the numbers n such that (n^k+1)/11 is a nonnegative integer. See also A267541. - Bruno Berselli, Jan 16 2016

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Tanya Khovanova, Recursive Sequences
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 989
Leo Tavares, Illustration: Triangular Lines
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008593, A017401, A017413, A045572, A267541.
Cf. A211013 (partial sums), A254322 (partial products).
Powers of the form (11*n+10)^m: this sequence (m=1), A017510 (m=2), A017511 (m=3), A017512 (m=4), A017513 (m=5), A017514 (m=6), A017515 (m=7), A017516 (m=8), A017517 (m=9), A017518 (m=10), A017519 (m=11), A017520 (m=12).
Cf. A008591, A005408.

List([0..60], n-> (11*n+10)); # G. C. Greubel, Oct 29 2019

[11*n+10: n in [0..60]]; // Vincenzo Librandi, Sep 18 2011

seq((11*n+10), n=0..60); # G. C. Greubel, Oct 29 2019

Range[10, 1000, 11] (* Vladimir Joseph Stephan Orlovsky, May 29 2011 *)
(11*Range[60] -1) (* G. C. Greubel, Oct 29 2019 *)

a(n)=11*n+10 \\ Charles R Greathouse IV, Jul 10 2016

def a(n): return 11*n + 10
print([a(n) for n in range(53)]) # Michael S. Branicky, Oct 21 2021

[(11*n+10) for n in (0..60)] # G. C. Greubel, Oct 29 2019

From G. C. Greubel, Oct 29 2019: (Start)
G.f.: (10 + x)/(1-x)^2.
E.g.f.: (10 + 11*x)*exp(x).
a(n) = 2*a(n-1) - a(n-2). (End)
a(n) = A008591(n+1) + A005408(n). - Leo Tavares, Oct 25 2022

A049211 a(n) = Product_{k=1..n} (9*k - 1); 9-factorial numbers.

Original entry on oeis.org

1, 8, 136, 3536, 123760, 5445440, 288608320, 17893715840, 1270453824640, 101636305971200, 9045631231436800, 886471860680806400, 94852489092846284800, 11002888734770169036800, 1375361091846271129600000, 184298386307400331366400000, 26354669241958247385395200000

Offset: 0

Wolfdieter Lang

G. C. Greubel, Table of n, a(n) for n = 0..325

Sequences of the form m^n*Pochhammer((m-1)/m, n): A000007 (m=1), A001147 (m=2), A008544 (m=3), A008545 (m=4), A008546 (m=5), A008543 (m=6), A049209 (m=7), A049210 (m=8), this sequence (m=9), A049212 (m=10), A254322 (m=11), A346896 (m=12).

Cf. A035022, A048994.

m:=9; [Round(m^n*Gamma(n +(m-1)/m)/Gamma((m-1)/m)): n in [0..20]]; // G. C. Greubel, Feb 08 2022

CoefficientList[Series[(1-9*x)^(-8/9),{x,0,20}],x] * Range[0,20]! (* Vaclav Kotesovec, Jan 28 2015 *)

a(n) = prod(k=1, n, 9*k-1); \\ Michel Marcus, Jan 08 2015

m=9; [m^n*rising_factorial((m-1)/m, n) for n in (0..20)] # G. C. Greubel, Feb 08 2022

a(n) = 8*A035022(n) = (9*n-1)(!^9), n >= 1, a(0) = 1.
a(n) = (-1)^n*Sum_{k=0..n} 9^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. - Mircea Merca, May 03 2012
a(n) = 9^n * Gamma(n+8/9) / Gamma(8/9). - Vaclav Kotesovec, Jan 28 2015
E.g.f: (1-9*x)^(-8/9). - Vaclav Kotesovec, Jan 28 2015
From Nikolaos Pantelidis, Dec 09 2020: (Start)
G.f.: 1/(1-8*x-72*x^2/(1-26*x-306*x^2/(1-44*x-702*x^2/(1-62*x-1260*x^2/(1-80*x-1980*x^2/(1-...)))))) (Jacobi continued fraction).
G.f.: 1/(1-8*x/(1-9*x/(1-17*x/(1-18*x/(1-26*x/(1-27*x/(1-35*x/(1-36*x/(1-44*x/(1-45*x/(1-...))))))))))) (Stieltjes continued fraction). (End)
From Nikolaos Pantelidis, Dec 19 2020: (Start)
G.f.: 1/G(0) where G(k) = 1 - (18*k+8)*x - 9*(k+1)*(9*k+8)*x^2/G(k+1) (continued fraction).
G.f.: 1/Q(0) where Q(k) = 1 - x*(9*k+8)/(1 - x*(9*k+9)/Q(k+1) ) (continued fraction). (End)
G.f.: hypergeometric2F0([1, 8/9], [--], 9*x). - G. C. Greubel, Feb 08 2022
Sum_{n>=0} 1/a(n) = 1 + (e/9)^(1/9)*(Gamma(8/9) - Gamma(8/9, 1/9)). - Amiram Eldar, Dec 21 2022

a(9) (originally given incorrectly as 1011636305971200) corrected by Peter Bala, Feb 20 2015
a(15)-a(16) from Vincenzo Librandi, Feb 20 2015
a(16) corrected and incorrect MAGMA program removed by Georg Fischer, May 10 2021

A049210 a(n) = -Product_{k=0..n} (8*k-1); octo-factorial numbers.

Original entry on oeis.org

1, 7, 105, 2415, 74865, 2919735, 137227545, 7547514975, 475493443425, 33760034483175, 2667042724170825, 232032717002861775, 22043108115271868625, 2270440135873002468375, 252018855081903273989625, 29990243754746489604765375, 3808760956852804179805202625

Offset: 0

Wolfdieter Lang

Seiichi Manyama, Table of n, a(n) for n = 0..333
Index entries for sequences related to factorial numbers.

Cf. A034975, A048994, A051187.

Sequences of the form m^n*Pochhammer((m-1)/m, n): A000007 (m=1), A001147 (m=2), A008544 (m=3), A008545 (m=4), A008546 (m=5), A008543 (m=6), A049209 (m=7), this sequence (m=8), A049211 (m=9), A049212 (m=10), A254322 (m=11), A346896 (m=12).

m:=8; [Round(m^n*Gamma(n +(m-1)/m)/Gamma((m-1)/m)): n in [0..30]]; // G. C. Greubel, Feb 16 2022

FoldList[Times,1,8*Range[20]-1] (* Harvey P. Dale, Aug 03 2014 *)
CoefficientList[Series[(1-8*x)^(-7/8),{x,0,20}],x] * Range[0,20]! (* Vaclav Kotesovec, Jan 28 2015 *)

a(n) = -prod(k=0, n, 8*k-1); \\ Michel Marcus, Jan 08 2015

m=8; [m^n*rising_factorial((m-1)/m, n) for n in (0..30)] # G. C. Greubel, Feb 16 2022

a(n) = 7*A034975(n) = (8*n-1)(!^8), n >= 1, a(0) = 1.
G.f.: 1/(1-7*x/(1-8*x/(1-15*x/(1-16*x/(1-23*x/(1-24*x/(1-31*x/(1-32*x/(1-... (continued fraction). - Philippe Deléham, Jan 07 2012
a(n) = (-1)^n*Sum_{k=0..n} 8^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. - Mircea Merca, May 03 2012
G.f.: ( 1 - 1/Q(0) )/x where Q(k) = 1 - x*(8*k-1)/(1 - x*(8*k+8)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Mar 20 2013
a(n) = 8^n*Gamma(n+7/8)/Gamma(7/8). - R. J. Mathar, Mar 20 2013
E.g.f: (1-8*x)^(-7/8). - Vaclav Kotesovec, Jan 28 2015
G.f.: 1/(1-7*x-56*x^2/(1-23*x-240*x^2/(1-39*x-552*x^2/(1-55*x-992*x^2/(1-71*x-1560*x^2/(1-... )))))) (Jacobi continued fraction). - Nikolaos Pantelidis, Dec 09 2020
G.f.: 1/G(0) where G(k) = 1 - (16*k+7)*x - 8*(k+1)*(8*k+7)*x^2/G(k+1); (continued fraction). - Nikolaos Pantelidis, Dec 19 2020
Sum_{n>=0} 1/a(n) = 1 + (e/8)^(1/8)*(Gamma(7/8) - Gamma(7/8, 1/8)). - Amiram Eldar, Dec 20 2022

A346896 Expansion of e.g.f.: (1-12*x)^(-11/12).

Original entry on oeis.org

1, 11, 253, 8855, 416185, 24554915, 1743398965, 144702114095, 13746700839025, 1470896989775675, 175036741783305325, 22929813173612997575, 3278963283826658653225, 508239308993132091249875, 84875964601853059238729125, 15192797663731697603732513375

Offset: 0

Nikolaos Pantelidis, Aug 06 2021

G. C. Greubel, Table of n, a(n) for n = 0..300

Sequences of the form m^n*Pochhammer((m-1)/m, n): A000007 (m=1), A001147 (m=2), A008544 (m=3), A008545 (m=4), A008546 (m=5), A008543 (m=6), A049209 (m=7), A049210 (m=8), A049211 (m=9), A049212 (m=10), A254322 (m=11), this sequence (m=12).

m:=12; [Round(m^n*Gamma(n +(m-1)/m)/Gamma((m-1)/m)): n in [0..20]]; // G. C. Greubel, Feb 16 2022

CoefficientList[Series[(1-12*x)^(-11/12),{x,0,20}], x] * Range[0, 20]!
FullSimplify[Table[12^n Gamma[n+11/12]/Gamma[11/12],{n,0,15}]] (* Stefano Spezia, Aug 07 2021 *)

m=12; [m^n*rising_factorial((m-1)/m, n) for n in (0..20)] # G. C. Greubel, Feb 16 2022

G.f.: 1/(1-11*x/(1-12*x/(1-23*x/(1-24*x/(1-35*x/(1-36*x/(1-47*x/(1-48*x/(1-59*x/(1-60*x/(1-...))))))))))) (Stieltjes continued fraction).
G.f.: 1/Q(0) where Q(k) = 1 - x*(12*k+11)/(1 - x*(12*k+12)/Q(k+1) ) (continued fraction).
G.f.: 1/(1-11*x-132*x^2/(1-35*x-552*x^2/(1-59*x-1260*x^2/(1-83*x-2256*x^2/(1-107*x-3540*x^2/(1-...)))))) (Jacobi continued fraction).
G.f.: 1/G(0) where G(k) = 1 - x*(24*k+11) - 12*(k+1)*(12*k+11)*x^2/G(k+1) (continued fraction).
a(n) = 12^n*Gamma(n+11/12)/Gamma(11/12). - Stefano Spezia, Aug 07 2021
Sum_{n>=0} 1/a(n) = 1 + (e/12)^(1/12)*(Gamma(11/12) - Gamma(11/12, 1/12)). - Amiram Eldar, Dec 22 2022

A020005 Nearest integer to Gamma(n + 10/11)/Gamma(10/11).

Original entry on oeis.org

1, 1, 2, 5, 20, 97, 573, 3956, 31285, 278721, 2761871, 30129503, 358814994, 4631975383, 64426566695, 960541539816, 15281342678897, 258393612570435, 4627594697852333, 87503608832116847, 1742117303112144502

Offset: 0

Simon Plouffe

nonn

Gamma(n + 10/11)/Gamma(10/11) = 1, 10/11, 210/121, 6720/1331, 288960/14641, 15603840/161051, 1014249600/1771561, ... - R. J. Mathar, Sep 04 2016

Shujing Lyu, Table of n, a(n) for n = 0..449

Cf. A254322, A020050, A020095.

[Round(Gamma(n +10/11)/Gamma(10/11)): n in [0..30]]; // G. C. Greubel, Jan 19 2018

Digits := 64:f := proc(n,x) round(GAMMA(n+x)/GAMMA(x)); end;

Table[Round[Gamma[n + #]/Gamma[#]] &[10/11], {n, 0, 20}] (* Michael De Vlieger, Apr 18 2016 *)

a(n) = round(gamma(n+10/11)/gamma(10/11)); \\ Michel Marcus, Apr 19 2016

cp's OEIS Frontend

A256890 Triangle T(n,k) = t(n-k, k); t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), where f(x) = x + 2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

SageMath

Formula

A049209 a(n) = -Product_{k=0..n} (7*k-1); sept-factorial numbers.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Sage

Formula

A017509 a(n) = 11*n + 10.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

Python

Sage

Formula

A049211 a(n) = Product_{k=1..n} (9*k - 1); 9-factorial numbers.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Sage

Formula

Extensions

A049210 a(n) = -Product_{k=0..n} (8*k-1); octo-factorial numbers.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Sage

Formula

A346896 Expansion of e.g.f.: (1-12*x)^(-11/12).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Sage

Formula

A020005 Nearest integer to Gamma(n + 10/11)/Gamma(10/11).

Views

A256890 Triangle T(n,k) = t(n-k, k); t(n,m) = f(m)t(n-1,m) + f(n)t(n,m-1), where f(x) = x + 2.