A211247 Irregular triangle read by rows: numbers b_m(i) related to Bernoulli and Euler polynomials.

2, 5, 4, 4, 2, 7, 13, 4, 6, 9, 2, 9, 26, 25, 4, 8, 20, 16, 2, 11, 43, 70, 41, 4, 10, 35, 50, 25, 2, 13, 64, 147, 155, 61, 4, 12, 54, 112, 105, 36, 2, 15, 89, 264, 406, 301, 85, 4, 14, 77, 210, 294, 196, 49, 2, 17, 118, 429, 870, 966, 532, 113, 4, 16, 104, 352, 660, 672, 336, 64, 2

Offset

2,1

Comments

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

It appears that every second row equals every second row of A034807. - Ralf Stephan, Oct 26 2013

Links

Table of n, a(n) for n=2..72.

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:
2
5 4
4 2
7 13 4
6 9 2
9 26 25 4
8 20 16 2
11 43 70 41 4
10 35 50 25 2
13 64 147 155 61 4
12 54 112 105 36 2
...

Prog

(PARI)
c(m, i) = binomial(m+1-i, i)*(m*m+m-2*i)/((m-i)*(m+1-i));
d(m, i) = binomial(m-i, i)*m/(m-i);
b(m, i) = if ( m%2==0, d(m, i), c(m, i) );
for (m=2, 16, for (i=1, ceil(m/2), print1( b(m, i), ", " ))) \\ Hugo Pfoertner, Nov 01 2017

Crossrefs

Cf. A034807, A211246, A267633.

Sequence in context: A266401 A083798 A197377 * A021397 A325941 A104658

Adjacent sequences: A211244 A211245 A211246 * A211248 A211249 A211250

Keyword

nonn,tabf

Author

N. J. A. Sloane, Apr 05 2012

Extensions

Corrected and extended by Hugo Pfoertner, Nov 01 2017

Status

approved