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A211246 Irregular triangle read by rows: numbers a_m(i) related to Bernoulli and Euler polynomials. 1
4, 3, 6, 8, 5, 5, 8, 19, 12, 7, 14, 7, 10, 34, 44, 16, 9, 27, 30, 9, 12, 53, 104, 85, 20, 11, 44, 77, 55, 11, 14, 76, 200, 259, 146, 24, 13, 65, 156, 182, 91, 13, 16, 103, 340, 606, 560, 231, 28, 15, 90, 275, 450, 378, 140, 15, 18, 134, 532, 1210, 1572, 1092, 344, 32 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

See the Sun (2008) reference for the (complicated) precise definition.

LINKS

Table of n, a(n) for n=2..65.

Zhi-Wei Sun, On sums of binomial coefficients and their applications, arXiv:math/0404385 [math.NT], 2004-2008.

Zhi-Wei Sun, On sums of binomial coefficients and their applications, Discrete Math. 308 (2008), no. 18, 4231--4245. MR2427754(2010d:05002).

EXAMPLE

Triangle begins:

4

3

6 8

5 5

8 19 12

7 14 7

10 34 44 16

9 27 30 9

12 53 104 85 20

11 44 77 55 11

14 76 200 259 146 24

...

MATHEMATICA

c[m_, i_] := Binomial[m-1-i, i] + 4 Binomial[m-i, i-1];

d[m_, i_] := Binomial[m-i, i] m/(m -i);

a[m_, i_] := If[EvenQ[m], c[m, i], d[m, i]];

Table[a[m, i], {m, 1, 16}, {i, 1, m/2}] // Flatten (* Jean-François Alcover, Oct 08 2018, from PARI *)

PROG

(PARI)

c(m, i) = binomial(m-1-i, i) + 4*binomial(m-i, i-1);

d(m, i) = binomial(m-i, i)*m / (m-i);

a(m, i) = if ( m%2 == 0, c(m, i), d(m, i) );

for (m=1, 16, for (i=1, floor(m/2), print1( a(m, i), ", "))) \\ Hugo Pfoertner, Nov 01 2017

CROSSREFS

Cf. A034807, A211247, A267633.

Sequence in context: A021700 A309516 A211362 * A197829 A187890 A305581

Adjacent sequences:  A211243 A211244 A211245 * A211247 A211248 A211249

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Apr 05 2012

EXTENSIONS

More terms from Hugo Pfoertner, Nov 01 2017

STATUS

approved

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Last modified January 25 03:49 EST 2020. Contains 331241 sequences. (Running on oeis4.)