A211246 Irregular triangle read by rows: numbers a_m(i) related to Bernoulli and Euler polynomials.

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

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