The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A172021 Start with the triangle A171661, reverse its rows, add missing powers of 2 at beginning of each row. 1
 1, 1, 2, 2, 1, 2, 4, 6, 6, 1, 2, 4, 8, 14, 20, 20, 1, 2, 4, 8, 16, 30, 50, 70, 70, 1, 2, 4, 8, 16, 32, 62, 112, 182, 252, 252, 1, 2, 4, 8, 16, 32, 64, 126, 238, 420, 672, 924, 924, 1, 2, 4, 8, 16, 32, 64, 128, 254, 492, 912, 1584, 2508, 3432, 3432 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Rows sum up to A030662 Triangle is a (mirrored) interspaced binomial transform of 1^n (see example). - Mark Dols, Jan 24 2010] T(n,k) is the number of k permutations of n (indistinguishable) objects of type I and n (indistinguishable) objects of type II. - Geoffrey Critzer, Mar 15 2010 Equivalently T(n,k) is the number of words length k from an alphabet of 2 letters with at most n occurrences of each letter. - Giovanni Artico, Aug 24 2013 T(n,k) is also the number of ways k persons can be accommodated into 2 rooms with at most n persons per room. - Giovanni Artico, Aug 24 2013 LINKS FORMULA E.g.f. for row n is: ( 1 + x + x^2/2! + ... + x^n/n! )^2. - Geoffrey Critzer, Mar 15 2010 EXAMPLE Triangle begins: ......1 ....1,2,2 ..1,2,4,6,6 1,2,4,8,14,20,20 From Mark Dols, Jan 24 2010: (Start) Interspaced binomial transform of 1^n: 1...1...1...1...1...1... ..2...2...2...2...2...2. 2...4...4...4...4...4... ..6...8...8...8...8...8. 6.. 14..16..16..16..16.. ..20..30..32..32..32..32 20..50..62..64..64..64.. (End) MAPLE seq(PolynomialTools:-CoefficientList((convert(taylor(exp(x), x, n+1), polynom)^2), x)*~[seq(i!, i=0..2 n)], n=0..10) # Giovanni Artico, Aug 30 2013 MATHEMATICA Table[CoefficientList[Series[(Sum[x^i/i!, {i, 0, m}])^2, {x, 0, 2 m}], x]*Table[n!, {n, 0, 2 m}], {m, 0, 10}] // Grid (* Geoffrey Critzer, Mar 15 2010 *) PROG (DERIVE) T(n, k):=POLY_COEFF(SUM(x^i/i!, i, 0, n)^2, x, k)·k! TABLE(VECTOR(T(v, u), u, 0, 2·v), v, 0, 10)  # Giovanni Artico, Aug 30 2013 CROSSREFS Cf. A030662, A171661, A171698, A004070. Sequence in context: A247495 A230290 A294783 * A325182 A215959 A209555 Adjacent sequences:  A172018 A172019 A172020 * A172022 A172023 A172024 KEYWORD nonn,tabf AUTHOR Mark Dols, Jan 22 2010 EXTENSIONS Definition rewritten by N. J. A. Sloane, Jan 23 2010 More terms from Mark Dols, Jan 24 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 1 08:44 EST 2021. Contains 349426 sequences. (Running on oeis4.)