A038210 -id:A038210 - cp's OEIS frontend

A099092 Riordan array (1,2+4x).

1, 0, 2, 0, 4, 4, 0, 0, 16, 8, 0, 0, 16, 48, 16, 0, 0, 0, 96, 128, 32, 0, 0, 0, 64, 384, 320, 64, 0, 0, 0, 0, 512, 1280, 768, 128, 0, 0, 0, 0, 256, 2560, 3840, 1792, 256, 0, 0, 0, 0, 0, 2560, 10240, 10752, 4096, 512, 0, 0, 0, 0, 0, 1024, 15360, 35840, 28672, 9216, 1024, 0, 0, 0

Offset: 0

Paul Barry, Sep 25 2004

Row sums are A063727. Diagonal sums are A052907.

The Riordan array (1, s+tx) defines T(n,k) = binomial(k,n-k)*s^k*(t/s)^(n-k). The row sums satisfy a(n) = s*a(n-1) + t*a(n-2) and the diagonal sums satisfy a(n) = s*a(n-2) + t*a(n-3).

			Rows begin
  {1},
  {0,  2},
  {0,  4,  4},
  {0,  0, 16,  8},
  {0,  0, 16, 48, 16}, ...

Cf. A026729, A038210, A052907, A063727, A113953.

Number triangle T(n,k) = binomial(k, n-k)*2^n; columns have g.f. (2x+4x^2)^k.

T(n,k) = A113953(n,k)*2^k = A026729(n,k)*2^n. - Philippe Deléham, Dec 11 2008

A137337 T(i,j) = (-1)^(i+j)(i+1)binomial(i,j)2^(i-j)4^j.

Original entry on oeis.org

1, -4, 8, 12, -48, 48, -32, 192, -384, 256, 80, -640, 1920, -2560, 1280, -192, 1920, -7680, 15360, -15360, 6144, 448, -5376, 26880, -71680, 107520, -86016, 28672, -1024, 14336, -86016, 286720, -573440, 688128, -458752, 131072, 2304, -36864, 258048, -1032192, 2580480, -4128768, 4128768, -2359296, 589824

Offset: 0

Roger L. Bagula, Apr 07 2008

Apart from signs, row i equals (i+1) times row i of A038210. - Joerg Arndt, Aug 07 2020

			Triangle starts:
1,
-4, 8,
12, -48, 48,
-32, 192, -384, 256,
80, -640, 1920, -2560, 1280,
-192, 1920, -7680, 15360, -15360, 6144,
448, -5376, 26880, -71680, 107520, -86016, 28672,
-1024, 14336, -86016, 286720, -573440, 688128, -458752, 131072,...

T(i,j) = (-1)^(i+j)*(i+1)*binomial(i,j)*2^(i-j)*4^j;
for(i=0,10,for(j=0,i,print1(T(i,j),", "));print()); \\ Joerg Arndt, Aug 07 2020

Corrected and edited by Joerg Arndt, Aug 07 2020

Definition corrected to match terms by Georg Fischer, Apr 28 2022

cp's OEIS Frontend

A099092 Riordan array (1,2+4x).

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A137337 T(i,j) = (-1)^(i+j)(i+1)binomial(i,j)2^(i-j)4^j.

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cp's OEIS Frontend

A099092 Riordan array (1,2+4x).

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula

A137337 T(i,j) = (-1)^(i+j)*(i+1)*binomial(i,j)*2^(i-j)*4^j.

Views

Author

Keywords

Comments

Examples

Programs

PARI

Extensions

A137337 T(i,j) = (-1)^(i+j)(i+1)binomial(i,j)2^(i-j)4^j.