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A135227 Triangle A000012 * A135225, read by rows. 2
1, 2, 1, 3, 2, 1, 4, 3, 3, 1, 5, 4, 6, 4, 1, 6, 5, 10, 10, 5, 1, 7, 6, 15, 20, 15, 6, 1, 8, 7, 21, 35, 35, 21, 7, 1, 9, 8, 28, 56, 70, 56, 28, 8, 1, 10, 9, 36, 84, 126, 126, 84, 36, 9, 1, 11, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1, 12, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums = A006127: (1, 3, 6, 11, 20, 37,...).

LINKS

G. C. Greubel, Rows n = 0..100 of triangle, flattened

FORMULA

A000012 * A135225 as infinite lower triangular matrices. Left border of 1's in Pascal's Triangle (A007318) is replaced with a column of (1,2,3,...).

T(n,k) = binomial(n,k), with T(n,0) = n+1. - G. C. Greubel, Nov 20 2019

EXAMPLE

First few rows of the triangle are:

  1;

  2, 1;

  3, 2,  1;

  4, 3,  3,  1;

  5, 4,  6,  4,  1;

  6, 5, 10, 10,  5, 1;

  7, 6, 15, 20, 15, 6, 1;

...

MAPLE

seq(seq( `if`(k=0, n+1, binomial(n, k)), k=0..n), n=0..12); # G. C. Greubel, Nov 20 2019

MATHEMATICA

Table[If[k==0, n+1, Binomial[n, k]], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 20 2019 *)

PROG

(PARI) T(n, k) = if(k==0, n+1, binomial(n, k)); \\ G. C. Greubel, Nov 20 2019

(MAGMA) [k eq 0 select n+1 else Binomial(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 20 2019

(Sage)

def T(n, k):

    if (k==0): return 1

    else: return binomial(n, k)

[[T(n, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Nov 20 2019

(GAP)

T:= function(n, k)

    if k=0 then return 1;

    else return Binomial(n, k);

    fi; end;

Flat(List([0..12], n-> List([0..n], k-> T(n, k) ))); # G. C. Greubel, Nov 20 2019

CROSSREFS

Cf. A006127, A007318, A135225.

Sequence in context: A255238 A212536 A188277 * A104325 A204925 A133084

Adjacent sequences:  A135224 A135225 A135226 * A135228 A135229 A135230

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Nov 23 2007

EXTENSIONS

More terms added by G. C. Greubel, Nov 20 2019

STATUS

approved

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Last modified December 8 17:01 EST 2021. Contains 349596 sequences. (Running on oeis4.)