A128936 a(n) = binomial(n, sum_digits_n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 55, 220, 715, 2002, 5005, 11440, 24310, 48620, 92378, 190, 1330, 7315, 33649, 134596, 480700, 1562275, 4686825, 13123110, 34597290, 4060, 31465, 201376, 1107568, 5379616, 23535820, 94143280, 348330136, 1203322288

Offset

0,11

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 1..1000 from G. C. Greubel)

Example

a(12) = binomial(12,3) = 220.

Maple

P:=proc(n) local a, i, k, w; for i from 1 by 1 to n do w:=0; k:=i; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; a:=binomial(i, w); print(a); od; end: P(100);
a:=proc(n) local nn, s: nn:=convert(n, base, 10): s:=sum(nn[j], j=1..nops(nn)): binomial(n, s): end: seq(a(n), n=0..38); # Emeric Deutsch, May 04 2007

Mathematica

Table[Binomial[n, Total[IntegerDigits[n]]], {n, 1, 40}] (* G. C. Greubel, Feb 10 2019 *)

Prog

(PARI) a(n) = binomial(n, sumdigits(n)); \\ Michel Marcus, Feb 10 2019
(Sage) [binomial(n, sum(int(d) for d in str(n))) for n in (1..40)] # G. C. Greubel, Feb 10 2019

Crossrefs

Cf. A007953.

Sequence in context: A008502 A008492 A023035 * A000582 A229890 A243744

Adjacent sequences: A128933 A128934 A128935 * A128937 A128938 A128939

Keyword

nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Apr 27 2007

Extensions

a(0)=1 prepended by Seiichi Manyama, Apr 24 2019

Status

approved